Решить уравнение:[latex] (\frac{1}{4}) ^{ \frac{4- x^{2} }{2} } = 8^{x} [/latex]

[latex]( \frac{1}{4}) ^{ \frac{4- x^{2} }{2} } =8 ^{x} [/latex] [latex]( \frac{1}{2 ^{2} } ) ^{ \frac{4- x^{2} }{2} } =2 ^{3x} [/latex] [latex]2 ^{-2* \frac{4- x^{2} }{2} } =2 ^{3x} [/latex] [latex] \frac{-2(4- x^{2} )}{2} =3x[/latex] [latex]-(4- x^{2} )=3x[/latex] [latex]-4+ x^{2} -3x=0[/latex] [latex] x^{2} -3x-4=0[/latex] D = (-3)² - 4· 1· (-4) = 9 + 16 = 25 [latex] \sqrt{D}=5 [/latex] [latex]x _{1} = \frac{3+5}{2}= \frac{8}{2} =4[/latex] [latex] x_{2} = \frac{3-5}{2} = \frac{-2}{2} =-1[/latex]