Решить уравнение [tex] 2^{ x^{2}-3 } [/tex] = [tex] 4^{x} [/tex]. Created by Simon026. algebra-ru

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Дмитрий1425 $2^{x^2 - 3} = 4^{x} \\ \\ 
2^{x^2 - 3} = 2^{2x} \\ \\ 
x^2 - 3 = 2x \\ \\ 
x^2 - 2x - 3 = 0 \\ \\ 
x^2 - 2x + 1 - 4 = 0 \\ \\ 
(x - 1)^2 - 2^2 = 0 \\ \\ 
(x - 1 - 2)(x - 1 + 2) = 0 \\ \\
x = -3 \ \ \ \ \ \ x = -1$

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$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
$

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