Найти значение выражения a^8-4*a^2-8*a-4еслиa=1/4 (a в степени 8 минус 4 умножить на a в квадрате минус 8 умножить на a минус 4еслиa равно 1 делить на 4) [Есть ответ!]

a^8-4*a^2-8*a-4еслиa=1/4 (упростите выражение)

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Решение

Вы ввели [src]
 8      2          
a  - 4*a  - 8*a - 4
$$a^{8} - 4 a^{2} - 8 a - 4$$
Подстановка условия [src]
a^8 - 4*a^2 - 8*a - 1*4 при a = 1/4
подставляем
 8      2          
a  - 4*a  - 8*a - 4
$$a^{8} - 4 a^{2} - 8 a - 4$$
      8            2
-4 + a  - 8*a - 4*a 
$$a^{8} - 4 a^{2} - 8 a - 4$$
переменные
a = 1/4
$$a = \frac{1}{4}$$
          8                    2
-4 + (1/4)  - 8*(1/4) - 4*(1/4) 
$$(1/4)^{8} - 4 (1/4)^{2} - 8 (1/4) - 4$$
     1              1 
-4 + -- - 8*1/4 - 4*--
      8              2
     4              4 
$$-4 - 2 - \frac{4}{16} + \left(\frac{1}{4}\right)^{8}$$
-409599 
--------
 65536  
$$- \frac{409599}{65536}$$
Степени [src]
      8            2
-4 + a  - 8*a - 4*a 
$$a^{8} - 4 a^{2} - 8 a - 4$$
Численный ответ [src]
-4.0 + a^8 - 4.0*a^2 - 8.0*a
Рациональный знаменатель [src]
      8            2
-4 + a  - 8*a - 4*a 
$$a^{8} - 4 a^{2} - 8 a - 4$$
Объединение рациональных выражений [src]
       /       /      6\\
-4 + a*\-8 + a*\-4 + a //
$$a \left(a \left(a^{6} - 4\right) - 8\right) - 4$$
Общее упрощение [src]
      8            2
-4 + a  - 8*a - 4*a 
$$a^{8} - 4 a^{2} - 8 a - 4$$
Собрать выражение [src]
      8      2      
-4 + a  - 4*a  - 8*a
$$a^{8} - 4 a^{2} - 8 a - 4$$
Комбинаторика [src]
/      4      \ /     4      \
\-2 + a  - 2*a/*\2 + a  + 2*a/
$$\left(a^{4} - 2 a - 2\right) \left(a^{4} + 2 a + 2\right)$$
Общий знаменатель [src]
      8            2
-4 + a  - 8*a - 4*a 
$$a^{8} - 4 a^{2} - 8 a - 4$$
Разложение на множители [src]
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$$\left(a + \left(\frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2} - \frac{\sqrt{- \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}} - 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}{2}\right)\right) 1 \left(a + \left(\frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2} + \frac{\sqrt{- \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}} - 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}{2}\right)\right) \left(a - \left(\frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}}{2}\right)\right) \left(a + \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} + \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2} + \frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2}\right)\right) \left(a - \left(\frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} - \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2}\right)\right) \left(a - \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}}{2} + \frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2}\right)\right) \left(a - \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} - \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2} + \frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2}\right)\right) \left(a - \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} + \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2} - \frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2}\right)\right)$$