Question

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

Answer 1

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

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