2*4^x-25*5^(2*x)-5*10^x>0 (неравенство) Учитель очень удивится увидев твоё верное решение 😼 Укажите решение неравенства: 2*4^x-25*5^(2*x)-5*10^x>0 (множество решений неравенства)
Решение
Подробное решение
Дано неравенство:− 5 ⋅ 1 0 x + 2 ⋅ 4 x − 25 ⋅ 5 2 x > 0 - 5 \cdot 10^{x} + 2 \cdot 4^{x} - 25 \cdot 5^{2 x} > 0 − 5 ⋅ 1 0 x + 2 ⋅ 4 x − 25 ⋅ 5 2 x > 0 − 5 ⋅ 1 0 x + 2 ⋅ 4 x − 25 ⋅ 5 2 x = 0 - 5 \cdot 10^{x} + 2 \cdot 4^{x} - 25 \cdot 5^{2 x} = 0 − 5 ⋅ 1 0 x + 2 ⋅ 4 x − 25 ⋅ 5 2 x = 0 x 1 = − 75.0161482956 x_{1} = -75.0161482956 x 1 = − 75.0161482956 x 2 = − 43.0161482956 x_{2} = -43.0161482956 x 2 = − 43.0161482956 x 3 = − 59.0161482956 x_{3} = -59.0161482956 x 3 = − 59.0161482956 x 4 = − 89.0161482956 x_{4} = -89.0161482956 x 4 = − 89.0161482956 x 5 = − 85.0161482956 x_{5} = -85.0161482956 x 5 = − 85.0161482956 x 6 = − 31.016149502 x_{6} = -31.016149502 x 6 = − 31.016149502 x 7 = − 107.016148296 x_{7} = -107.016148296 x 7 = − 107.016148296 x 8 = − 95.0161482956 x_{8} = -95.0161482956 x 8 = − 95.0161482956 x 9 = − 35.0161483265 x_{9} = -35.0161483265 x 9 = − 35.0161483265 x 10 = − 67.0161482956 x_{10} = -67.0161482956 x 10 = − 67.0161482956 x 11 = − 47.0161482956 x_{11} = -47.0161482956 x 11 = − 47.0161482956 x 12 = − 103.016148296 x_{12} = -103.016148296 x 12 = − 103.016148296 x 13 = − 51.0161482956 x_{13} = -51.0161482956 x 13 = − 51.0161482956 x 14 = − 71.0161482956 x_{14} = -71.0161482956 x 14 = − 71.0161482956 x 15 = − 99.0161482956 x_{15} = -99.0161482956 x 15 = − 99.0161482956 x 16 = − 69.0161482956 x_{16} = -69.0161482956 x 16 = − 69.0161482956 x 17 = − 81.0161482956 x_{17} = -81.0161482956 x 17 = − 81.0161482956 x 18 = − 101.016148296 x_{18} = -101.016148296 x 18 = − 101.016148296 x 19 = − 39.0161482964 x_{19} = -39.0161482964 x 19 = − 39.0161482964 x 20 = − 21.0281212285 x_{20} = -21.0281212285 x 20 = − 21.0281212285 x 21 = − 87.0161482956 x_{21} = -87.0161482956 x 21 = − 87.0161482956 x 22 = − 115.016148296 x_{22} = -115.016148296 x 22 = − 115.016148296 x 23 = − 33.0161484886 x_{23} = -33.0161484886 x 23 = − 33.0161484886 x 24 = − 105.016148296 x_{24} = -105.016148296 x 24 = − 105.016148296 x 25 = − 45.0161482956 x_{25} = -45.0161482956 x 25 = − 45.0161482956 x 26 = − 65.0161482956 x_{26} = -65.0161482956 x 26 = − 65.0161482956 x 27 = − 111.016148296 x_{27} = -111.016148296 x 27 = − 111.016148296 x 28 = − 41.0161482957 x_{28} = -41.0161482957 x 28 = − 41.0161482957 x 29 = − 83.0161482956 x_{29} = -83.0161482956 x 29 = − 83.0161482956 x 30 = − 73.0161482956 x_{30} = -73.0161482956 x 30 = − 73.0161482956 x 31 = − 53.0161482956 x_{31} = -53.0161482956 x 31 = − 53.0161482956 x 32 = − 79.0161482956 x_{32} = -79.0161482956 x 32 = − 79.0161482956 x 33 = − 93.0161482956 x_{33} = -93.0161482956 x 33 = − 93.0161482956 x 34 = − 23.0180009193 x_{34} = -23.0180009193 x 34 = − 23.0180009193 x 35 = − 55.0161482956 x_{35} = -55.0161482956 x 35 = − 55.0161482956 x 36 = − 57.0161482956 x_{36} = -57.0161482956 x 36 = − 57.0161482956 x 37 = − 77.0161482956 x_{37} = -77.0161482956 x 37 = − 77.0161482956 x 38 = − 113.016148296 x_{38} = -113.016148296 x 38 = − 113.016148296 x 39 = − 63.0161482956 x_{39} = -63.0161482956 x 39 = − 63.0161482956 x 40 = − 97.0161482956 x_{40} = -97.0161482956 x 40 = − 97.0161482956 x 41 = − 37.0161483006 x_{41} = -37.0161483006 x 41 = − 37.0161483006 x 42 = − 109.016148296 x_{42} = -109.016148296 x 42 = − 109.016148296 x 43 = − 27.0161954288 x_{43} = -27.0161954288 x 43 = − 27.0161954288 x 44 = − 29.0161558359 x_{44} = -29.0161558359 x 44 = − 29.0161558359 x 45 = − 91.0161482956 x_{45} = -91.0161482956 x 45 = − 91.0161482956 x 46 = − 49.0161482956 x_{46} = -49.0161482956 x 46 = − 49.0161482956 x 47 = − 1.75647079737 x_{47} = -1.75647079737 x 47 = − 1.75647079737 x 48 = − 61.0161482956 x_{48} = -61.0161482956 x 48 = − 61.0161482956 x 49 = − 25.0164431309 x_{49} = -25.0164431309 x 49 = − 25.0164431309 x 1 = − 75.0161482956 x_{1} = -75.0161482956 x 1 = − 75.0161482956 x 2 = − 43.0161482956 x_{2} = -43.0161482956 x 2 = − 43.0161482956 x 3 = − 59.0161482956 x_{3} = -59.0161482956 x 3 = − 59.0161482956 x 4 = − 89.0161482956 x_{4} = -89.0161482956 x 4 = − 89.0161482956 x 5 = − 85.0161482956 x_{5} = -85.0161482956 x 5 = − 85.0161482956 x 6 = − 31.016149502 x_{6} = -31.016149502 x 6 = − 31.016149502 x 7 = − 107.016148296 x_{7} = -107.016148296 x 7 = − 107.016148296 x 8 = − 95.0161482956 x_{8} = -95.0161482956 x 8 = − 95.0161482956 x 9 = − 35.0161483265 x_{9} = -35.0161483265 x 9 = − 35.0161483265 x 10 = − 67.0161482956 x_{10} = -67.0161482956 x 10 = − 67.0161482956 x 11 = − 47.0161482956 x_{11} = -47.0161482956 x 11 = − 47.0161482956 x 12 = − 103.016148296 x_{12} = -103.016148296 x 12 = − 103.016148296 x 13 = − 51.0161482956 x_{13} = -51.0161482956 x 13 = − 51.0161482956 x 14 = − 71.0161482956 x_{14} = -71.0161482956 x 14 = − 71.0161482956 x 15 = − 99.0161482956 x_{15} = -99.0161482956 x 15 = − 99.0161482956 x 16 = − 69.0161482956 x_{16} = -69.0161482956 x 16 = − 69.0161482956 x 17 = − 81.0161482956 x_{17} = -81.0161482956 x 17 = − 81.0161482956 x 18 = − 101.016148296 x_{18} = -101.016148296 x 18 = − 101.016148296 x 19 = − 39.0161482964 x_{19} = -39.0161482964 x 19 = − 39.0161482964 x 20 = − 21.0281212285 x_{20} = -21.0281212285 x 20 = − 21.0281212285 x 21 = − 87.0161482956 x_{21} = -87.0161482956 x 21 = − 87.0161482956 x 22 = − 115.016148296 x_{22} = -115.016148296 x 22 = − 115.016148296 x 23 = − 33.0161484886 x_{23} = -33.0161484886 x 23 = − 33.0161484886 x 24 = − 105.016148296 x_{24} = -105.016148296 x 24 = − 105.016148296 x 25 = − 45.0161482956 x_{25} = -45.0161482956 x 25 = − 45.0161482956 x 26 = − 65.0161482956 x_{26} = -65.0161482956 x 26 = − 65.0161482956 x 27 = − 111.016148296 x_{27} = -111.016148296 x 27 = − 111.016148296 x 28 = − 41.0161482957 x_{28} = -41.0161482957 x 28 = − 41.0161482957 x 29 = − 83.0161482956 x_{29} = -83.0161482956 x 29 = − 83.0161482956 x 30 = − 73.0161482956 x_{30} = -73.0161482956 x 30 = − 73.0161482956 x 31 = − 53.0161482956 x_{31} = -53.0161482956 x 31 = − 53.0161482956 x 32 = − 79.0161482956 x_{32} = -79.0161482956 x 32 = − 79.0161482956 x 33 = − 93.0161482956 x_{33} = -93.0161482956 x 33 = − 93.0161482956 x 34 = − 23.0180009193 x_{34} = -23.0180009193 x 34 = − 23.0180009193 x 35 = − 55.0161482956 x_{35} = -55.0161482956 x 35 = − 55.0161482956 x 36 = − 57.0161482956 x_{36} = -57.0161482956 x 36 = − 57.0161482956 x 37 = − 77.0161482956 x_{37} = -77.0161482956 x 37 = − 77.0161482956 x 38 = − 113.016148296 x_{38} = -113.016148296 x 38 = − 113.016148296 x 39 = − 63.0161482956 x_{39} = -63.0161482956 x 39 = − 63.0161482956 x 40 = − 97.0161482956 x_{40} = -97.0161482956 x 40 = − 97.0161482956 x 41 = − 37.0161483006 x_{41} = -37.0161483006 x 41 = − 37.0161483006 x 42 = − 109.016148296 x_{42} = -109.016148296 x 42 = − 109.016148296 x 43 = − 27.0161954288 x_{43} = -27.0161954288 x 43 = − 27.0161954288 x 44 = − 29.0161558359 x_{44} = -29.0161558359 x 44 = − 29.0161558359 x 45 = − 91.0161482956 x_{45} = -91.0161482956 x 45 = − 91.0161482956 x 46 = − 49.0161482956 x_{46} = -49.0161482956 x 46 = − 49.0161482956 x 47 = − 1.75647079737 x_{47} = -1.75647079737 x 47 = − 1.75647079737 x 48 = − 61.0161482956 x_{48} = -61.0161482956 x 48 = − 61.0161482956 x 49 = − 25.0164431309 x_{49} = -25.0164431309 x 49 = − 25.0164431309 x 22 = − 115.016148296 x_{22} = -115.016148296 x 22 = − 115.016148296 x 38 = − 113.016148296 x_{38} = -113.016148296 x 38 = − 113.016148296 x 27 = − 111.016148296 x_{27} = -111.016148296 x 27 = − 111.016148296 x 42 = − 109.016148296 x_{42} = -109.016148296 x 42 = − 109.016148296 x 7 = − 107.016148296 x_{7} = -107.016148296 x 7 = − 107.016148296 x 24 = − 105.016148296 x_{24} = -105.016148296 x 24 = − 105.016148296 x 12 = − 103.016148296 x_{12} = -103.016148296 x 12 = − 103.016148296 x 18 = − 101.016148296 x_{18} = -101.016148296 x 18 = − 101.016148296 x 15 = − 99.0161482956 x_{15} = -99.0161482956 x 15 = − 99.0161482956 x 40 = − 97.0161482956 x_{40} = -97.0161482956 x 40 = − 97.0161482956 x 8 = − 95.0161482956 x_{8} = -95.0161482956 x 8 = − 95.0161482956 x 33 = − 93.0161482956 x_{33} = -93.0161482956 x 33 = − 93.0161482956 x 45 = − 91.0161482956 x_{45} = -91.0161482956 x 45 = − 91.0161482956 x 4 = − 89.0161482956 x_{4} = -89.0161482956 x 4 = − 89.0161482956 x 21 = − 87.0161482956 x_{21} = -87.0161482956 x 21 = − 87.0161482956 x 5 = − 85.0161482956 x_{5} = -85.0161482956 x 5 = − 85.0161482956 x 29 = − 83.0161482956 x_{29} = -83.0161482956 x 29 = − 83.0161482956 x 17 = − 81.0161482956 x_{17} = -81.0161482956 x 17 = − 81.0161482956 x 32 = − 79.0161482956 x_{32} = -79.0161482956 x 32 = − 79.0161482956 x 37 = − 77.0161482956 x_{37} = -77.0161482956 x 37 = − 77.0161482956 x 1 = − 75.0161482956 x_{1} = -75.0161482956 x 1 = − 75.0161482956 x 30 = − 73.0161482956 x_{30} = -73.0161482956 x 30 = − 73.0161482956 x 14 = − 71.0161482956 x_{14} = -71.0161482956 x 14 = − 71.0161482956 x 16 = − 69.0161482956 x_{16} = -69.0161482956 x 16 = − 69.0161482956 x 10 = − 67.0161482956 x_{10} = -67.0161482956 x 10 = − 67.0161482956 x 26 = − 65.0161482956 x_{26} = -65.0161482956 x 26 = − 65.0161482956 x 39 = − 63.0161482956 x_{39} = -63.0161482956 x 39 = − 63.0161482956 x 48 = − 61.0161482956 x_{48} = -61.0161482956 x 48 = − 61.0161482956 x 3 = − 59.0161482956 x_{3} = -59.0161482956 x 3 = − 59.0161482956 x 36 = − 57.0161482956 x_{36} = -57.0161482956 x 36 = − 57.0161482956 x 35 = − 55.0161482956 x_{35} = -55.0161482956 x 35 = − 55.0161482956 x 31 = − 53.0161482956 x_{31} = -53.0161482956 x 31 = − 53.0161482956 x 13 = − 51.0161482956 x_{13} = -51.0161482956 x 13 = − 51.0161482956 x 46 = − 49.0161482956 x_{46} = -49.0161482956 x 46 = − 49.0161482956 x 11 = − 47.0161482956 x_{11} = -47.0161482956 x 11 = − 47.0161482956 x 25 = − 45.0161482956 x_{25} = -45.0161482956 x 25 = − 45.0161482956 x 2 = − 43.0161482956 x_{2} = -43.0161482956 x 2 = − 43.0161482956 x 28 = − 41.0161482957 x_{28} = -41.0161482957 x 28 = − 41.0161482957 x 19 = − 39.0161482964 x_{19} = -39.0161482964 x 19 = − 39.0161482964 x 41 = − 37.0161483006 x_{41} = -37.0161483006 x 41 = − 37.0161483006 x 9 = − 35.0161483265 x_{9} = -35.0161483265 x 9 = − 35.0161483265 x 23 = − 33.0161484886 x_{23} = -33.0161484886 x 23 = − 33.0161484886 x 6 = − 31.016149502 x_{6} = -31.016149502 x 6 = − 31.016149502 x 44 = − 29.0161558359 x_{44} = -29.0161558359 x 44 = − 29.0161558359 x 43 = − 27.0161954288 x_{43} = -27.0161954288 x 43 = − 27.0161954288 x 49 = − 25.0164431309 x_{49} = -25.0164431309 x 49 = − 25.0164431309 x 34 = − 23.0180009193 x_{34} = -23.0180009193 x 34 = − 23.0180009193 x 20 = − 21.0281212285 x_{20} = -21.0281212285 x 20 = − 21.0281212285 x 47 = − 1.75647079737 x_{47} = -1.75647079737 x 47 = − 1.75647079737 x 0 < x 22 x_{0} < x_{22} x 0 < x 22 x 0 = x 22 − 1 10 x_{0} = x_{22} - \frac{1}{10} x 0 = x 22 − 10 1 − 115.116148296 -115.116148296 − 115.116148296 − 115.116148296 -115.116148296 − 115.116148296 − 5 ⋅ 1 0 x + 2 ⋅ 4 x − 25 ⋅ 5 2 x > 0 - 5 \cdot 10^{x} + 2 \cdot 4^{x} - 25 \cdot 5^{2 x} > 0 − 5 ⋅ 1 0 x + 2 ⋅ 4 x − 25 ⋅ 5 2 x > 0 -115.116148296 2*-115.116148296 -115.116148296
2*4 - 25*5 - 5*10 > 0 9.86740038811382e-70 > 0 x < − 115.016148296 x < -115.016148296 x < − 115.016148296 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
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x22 x38 x27 x42 x7 x24 x12 x18 x15 x40 x8 x33 x45 x4 x21 x5 x29 x17 x32 x37 x1 x30 x14 x16 x10 x26 x39 x48 x3 x36 x35 x31 x13 x46 x11 x25 x2 x28 x19 x41 x9 x23 x6 x44 x43 x49 x34 x20 x47 x < − 115.016148296 x < -115.016148296 x < − 115.016148296 x > − 113.016148296 ∧ x < − 111.016148296 x > -113.016148296 \wedge x < -111.016148296 x > − 113.016148296 ∧ x < − 111.016148296 x > − 109.016148296 ∧ x < − 107.016148296 x > -109.016148296 \wedge x < -107.016148296 x > − 109.016148296 ∧ x < − 107.016148296 x > − 105.016148296 ∧ x < − 103.016148296 x > -105.016148296 \wedge x < -103.016148296 x > − 105.016148296 ∧ x < − 103.016148296 x > − 101.016148296 ∧ x < − 99.0161482956 x > -101.016148296 \wedge x < -99.0161482956 x > − 101.016148296 ∧ x < − 99.0161482956 x > − 97.0161482956 ∧ x < − 95.0161482956 x > -97.0161482956 \wedge x < -95.0161482956 x > − 97.0161482956 ∧ x < − 95.0161482956 x > − 93.0161482956 ∧ x < − 91.0161482956 x > -93.0161482956 \wedge x < -91.0161482956 x > − 93.0161482956 ∧ x < − 91.0161482956 x > − 89.0161482956 ∧ x < − 87.0161482956 x > -89.0161482956 \wedge x < -87.0161482956 x > − 89.0161482956 ∧ x < − 87.0161482956 x > − 85.0161482956 ∧ x < − 83.0161482956 x > -85.0161482956 \wedge x < -83.0161482956 x > − 85.0161482956 ∧ x < − 83.0161482956 x > − 81.0161482956 ∧ x < − 79.0161482956 x > -81.0161482956 \wedge x < -79.0161482956 x > − 81.0161482956 ∧ x < − 79.0161482956 x > − 77.0161482956 ∧ x < − 75.0161482956 x > -77.0161482956 \wedge x < -75.0161482956 x > − 77.0161482956 ∧ x < − 75.0161482956 x > − 73.0161482956 ∧ x < − 71.0161482956 x > -73.0161482956 \wedge x < -71.0161482956 x > − 73.0161482956 ∧ x < − 71.0161482956 x > − 69.0161482956 ∧ x < − 67.0161482956 x > -69.0161482956 \wedge x < -67.0161482956 x > − 69.0161482956 ∧ x < − 67.0161482956 x > − 65.0161482956 ∧ x < − 63.0161482956 x > -65.0161482956 \wedge x < -63.0161482956 x > − 65.0161482956 ∧ x < − 63.0161482956 x > − 61.0161482956 ∧ x < − 59.0161482956 x > -61.0161482956 \wedge x < -59.0161482956 x > − 61.0161482956 ∧ x < − 59.0161482956 x > − 57.0161482956 ∧ x < − 55.0161482956 x > -57.0161482956 \wedge x < -55.0161482956 x > − 57.0161482956 ∧ x < − 55.0161482956 x > − 53.0161482956 ∧ x < − 51.0161482956 x > -53.0161482956 \wedge x < -51.0161482956 x > − 53.0161482956 ∧ x < − 51.0161482956 x > − 49.0161482956 ∧ x < − 47.0161482956 x > -49.0161482956 \wedge x < -47.0161482956 x > − 49.0161482956 ∧ x < − 47.0161482956 x > − 45.0161482956 ∧ x < − 43.0161482956 x > -45.0161482956 \wedge x < -43.0161482956 x > − 45.0161482956 ∧ x < − 43.0161482956 x > − 41.0161482957 ∧ x < − 39.0161482964 x > -41.0161482957 \wedge x < -39.0161482964 x > − 41.0161482957 ∧ x < − 39.0161482964 x > − 37.0161483006 ∧ x < − 35.0161483265 x > -37.0161483006 \wedge x < -35.0161483265 x > − 37.0161483006 ∧ x < − 35.0161483265 x > − 33.0161484886 ∧ x < − 31.016149502 x > -33.0161484886 \wedge x < -31.016149502 x > − 33.0161484886 ∧ x < − 31.016149502 x > − 29.0161558359 ∧ x < − 27.0161954288 x > -29.0161558359 \wedge x < -27.0161954288 x > − 29.0161558359 ∧ x < − 27.0161954288 x > − 25.0164431309 ∧ x < − 23.0180009193 x > -25.0164431309 \wedge x < -23.0180009193 x > − 25.0164431309 ∧ x < − 23.0180009193 x > − 21.0281212285 ∧ x < − 1.75647079737 x > -21.0281212285 \wedge x < -1.75647079737 x > − 21.0281212285 ∧ x < − 1.75647079737
Решение неравенства на графике
5 0 1 2 3 4 -7 -6 -5 -4 -3 -2 -1 -20 20
