Question

Помогите пожалуйста !!! 11 класс!!!!11•9^х-7•15^х-4•25^х=0

Answer 1

$11*frac{9^{x} }{25^{x} }-7*frac{15^{x} }{25^{x}}-4*frac{25^{x} }{25^{x} }=0\\11*(frac{3}{5})^{2x}-7*(frac{3}{5})^{x} -4=0\\(frac{3}{5})^{x}=m,m>0$

$11m^{2} -7m-4=0\\D=(-7)^{2}-4*11*(-4)=49+176=225=15^{2}\\m_{1}=frac{7+15}{22}=1\\m_{2}=frac{7-15}{22} =-frac{4}{11}<0\\(frac{3}{5} )^{x}=1\\(frac{3}{5})^{x}=(frac{3}{5})^{0}\\x=0$