Question

Решить показательное уравнение

Answer 1

$4^{3x^2+x} - 8 = 8^{x^2+x/3}*2\\4^{3x^2+x} - 8 = 2^{3x^2+x}*2\\2^{3x^2+x} = y\\4^{3x^2+x} = (2^{3x^2+x})^2 = y^2\\y^2 - 8 = 2y\\y^2 - 2y - 8 = 0\\y_{1} *y_{2} = -8\\y_{1} + y_{2} = 2\\y_{1} = 4\\y_{2} = -2\\2^{3x^2+x}=4\\2^{3x^2+x}=2^2\\3x^2+x=2\\3x^2+x-2=0\\x_{1}*x_{2}=-2/3\\x_{1}+x_{2}=-1/3\\x_{1}=2/3\\x_{2}=-1$