Question

Решить уравнение
$2^{ x^{2}-3 }$ = $4^{x}$

Answer 1

$2^{x^2-3}=4^x \ 2^{x^2-3}=2 ^{2x} \ x^2-3=2x \ x^2-3-2x=0 \ x^2-2x-3=0 \ D_{1} =(- frac{b}{2} )^2-ac \ D_{1}=4 \ x= frac{- frac{b}{2}+- sqrt{D} }{a} \ x=-1 x=3$

Answer 2

$2^{x^2 - 3} = 4^{x} \ \ 2^{x^2 - 3} = 2^{2x} \ \ x^2 - 3 = 2x \ \ x^2 - 2x - 3 = 0 \ \ x^2 - 2x + 1 - 4 = 0 \ \ (x - 1)^2 - 2^2 = 0 \ \ (x - 1 - 2)(x - 1 + 2) = 0 \ \ x = -3 x = -1$