Question

Решить уравнение$2^{x^2} *(\frac{1}{2} )^{\frac{1}{4} x} =\sqrt[4]{8}$

Answer 1

$2^{x^{2} } *(\frac{1}{2})^{\frac{1}{4} x}=\sqrt[4]{8} \\ \\ 2^{x^{2} } *2^{-\frac{1}{4} x}=\sqrt[4]{2^{3} } \\ \\ 2^{x^{2} } *2^{-\frac{1}{4} x}=2^{\frac{3}{4} } \\ \\ x^{2} -\frac{1}{4}x =\frac{3}{4} \\ \\ 4x^{2} -x=3\\ \\ 4x^{2} -x-3=0\\ \\ D=1^{2} +4*4*3=49\\ \\ x_{1} =\frac{1+7}{8} =1\\ \\ x_{2} =\frac{1-7}{8} =-\frac{7}{8}$