Question

Решите уравнение:
(2x^3)^5*(2x^2)^4:2*(4x^5)^4=27

Answer 1

Ответ:

$x = \frac {3} {\sqrt [3] {2}}$

Объяснение:

$\frac {(2x^3)^5\cdot (2x^2)^4}{(4x^5)^4} = 27 \\ \frac {2^5x^{15}\cdot 2^4x^8}{4^4x^{20}} = 27 \\ \frac {2^9x^{23}}{2^8x^{20}} = 27 \\ 2x^3 = 27 \\ x^3-\frac {27}{2}=0 \\ (x - \frac {3}{\sqrt [3]{2}})(x^2+\frac {3x}{\sqrt [3]{2}} + \frac {9}{\sqrt [3]{4}}) \\ x = \frac {3}{\sqrt [3]{2}}$