(2*r)^2=(12*sqrt(5)/5)^2+ ... ^2 12*sqrt(5)*x=h*r s=h*r
Решение
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[src]
2
/ ___\
2 |12*\/ 5 | 2
(2*r) = |--------| + (2*x)
\ 5 /
$$\left(2 r\right)^{2} = \left(2 x\right)^{2} + \left(\frac{12 \sqrt{5}}{5}\right)^{2}$$
2 2 2 h = (5*x) - r
$$h^{2} = - r^{2} + \left(5 x\right)^{2}$$
___ 12*\/ 5 *x = h*r
$$12 \sqrt{5} x = h r$$
s = h*r
$$s = h r$$
Быстрый ответ
$$s_{1} = 6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$x_{1} = \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
$$h_{1} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
$$r_{1} = - \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
=
$$6 \sqrt{231 + 15 \sqrt{241}}$$
=
129.224820897459
$$x_{1} = \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
4.81592473178257
$$h_{1} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
-23.4400329464931
$$r_{1} = - \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
-5.51299655561248
$$s_{2} = - 6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$- 6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$x_{2} = - \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
$$h_{2} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
$$r_{2} = \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
=
$$- 6 \sqrt{231 + 15 \sqrt{241}}$$
=
-129.224820897459
$$x_{2} = - \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
-4.81592473178257
$$h_{2} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- 25 \sqrt{2} + \sqrt{482}\right)$$
=
-23.4400329464931
$$r_{2} = \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
5.51299655561248
$$s_{3} = - 6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$- 6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$x_{3} = - \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
$$h_{3} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
$$r_{3} = - \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
=
$$- 6 \sqrt{231 + 15 \sqrt{241}}$$
=
-129.224820897459
$$x_{3} = - \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
-4.81592473178257
$$h_{3} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
23.4400329464931
$$r_{3} = - \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
-5.51299655561248
$$s_{4} = 6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$6 \sqrt{231 + 15 \sqrt{241}}$$
=
$$x_{4} = \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
$$h_{4} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
$$r_{4} = \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
=
$$6 \sqrt{231 + 15 \sqrt{241}}$$
=
129.224820897459
$$x_{4} = \sqrt{\frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{1155 + 75 \sqrt{241}}$$
=
4.81592473178257
$$h_{4} = \frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{1565 + 101 \sqrt{241}} \left(- \sqrt{482} + 25 \sqrt{2}\right)$$
=
23.4400329464931
$$r_{4} = \sqrt{\frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{3 \sqrt{241} + 75}$$
=
5.51299655561248
$$s_{5} = 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$x_{5} = i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
$$h_{5} = - \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$- \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$r_{5} = - \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
=
$$6 \sqrt{- 15 \sqrt{241} + 231}$$
=
8.18867119747843*i
$$x_{5} = i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
0.305173757382606*i
$$h_{5} = - \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$- \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
-3.07166803751324*i
$$r_{5} = - \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
-2.66587114801241
$$s_{6} = - 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$- 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$x_{6} = - i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
$$h_{6} = - \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$- \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$r_{6} = \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
=
$$- 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
-8.18867119747843*i
$$x_{6} = - i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
-0.305173757382606*i
$$h_{6} = - \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$- \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
-3.07166803751324*i
$$r_{6} = \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
2.66587114801241
$$s_{7} = - 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$- 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$x_{7} = - i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
$$h_{7} = \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$r_{7} = - \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
=
$$- 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
-8.18867119747843*i
$$x_{7} = - i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$- \frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
-0.305173757382606*i
$$h_{7} = \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
3.07166803751324*i
$$r_{7} = - \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$- \frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
-2.66587114801241
$$s_{8} = 6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$6 \sqrt{- 15 \sqrt{241} + 231}$$
=
$$x_{8} = i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
$$h_{8} = \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$r_{8} = \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
=
$$6 \sqrt{- 15 \sqrt{241} + 231}$$
=
8.18867119747843*i
$$x_{8} = i \sqrt{- \frac{231}{20} + \frac{3 \sqrt{241}}{4}}$$
=
$$\frac{1}{10} \sqrt{- 75 \sqrt{241} + 1155}$$
=
0.305173757382606*i
$$h_{8} = \frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
$$\frac{1}{32} \sqrt{- 101 \sqrt{241} + 1565} \left(\sqrt{482} + 25 \sqrt{2}\right)$$
=
3.07166803751324*i
$$r_{8} = \sqrt{- \frac{3 \sqrt{241}}{4} + \frac{75}{4}}$$
=
$$\frac{1}{2} \sqrt{- 3 \sqrt{241} + 75}$$
=
2.66587114801241
Численный ответ
[src]
h1 = 23.44003294649307 r1 = -5.512996555612475 s1 = -129.2248208974592 x1 = -4.81592473178257
h2 = -23.44003294649307 r2 = -5.512996555612475 s2 = 129.2248208974592 x2 = 4.81592473178257
h3 = 23.44003294649307 r3 = 5.512996555612475 s3 = 129.2248208974592 x3 = 4.81592473178257