Question

Решите уравнение)))))))​

Answer 1

$9^{x^{2}-x-5}+6^{x^{2}-x-4 }-180*4^{x^{2}-x-7 } =0\\\\9^{x^{2}-x-7 }*9^{2}+6^{x^{2}-x-7}*6^{3}-180*4^{x^{2}-x-7}=0|:4^{x^{2}-x-7 }>0\\\\81*(\frac{9}{4})^{x^{2}-x-7 }+216*(\frac{6}{4})^{x^{2}-x-7 }-180=0\\\\9*((\frac{3}{2}) ^{x^{2}-x-7 })^{2}+24*(\frac{3}{2})^{x^{2}-x-7 }-20=0$

$(\frac{3}{2})^{x^{2}-x-7 }=m,m>0\\\\9m^{2}+24m-20=0\\\\D=24^{2}-4*9*(-20)=576+720=1296=36^{2}\\\\m_{1}=\frac{-24+36}{18}=\frac{12}{18}=\frac{2}{3}\\\\m_{2}=\frac{-24-36}{18}=-\frac{60}{18}<0-neyd\\\\(\frac{3}{2})^{x^{2}-x-7 }=\frac{2}{3}$

$(\frac{3}{2})^{x^{2}-x-7 }=(\frac{3}{2})^{-1}\\\\x^{2}-x-7=-1\\\\x^{2}-x-6=0\\\\x_{1}=-2\\\\x_{2}=3\\\\Otvet:\boxed{-2;3}$