Question

11•9^х-7•15^х-4•25^х=0

Answer 1

$\displaystyle 11*9^x-7*15^x-4*25^x=0\\\\11*3^{2x}-7*(3*5)^x-4*5^{2x}=0|:5^{2x}\\\\11*(\frac{3}{5})^{2x}-7*(\frac{3^x*5^x}{5^{2x}})-4=0\\\\11*(\frac{3}{5})^{2x}-7*(\frac{3}{5})^x -4=0\\\\(\frac{3}{5})^x=t\\\\11t^2-7t-4=0\\\\D=49+4*4*11=49+176=225=15^2\\\\t_{1.2}=\frac{7\pm 15}{22}\\\\t_1=1; t_2=-\frac{4}{11}\\\\(\frac{3}{5})^x\neq -\frac{4}{11}\\\\(\frac{3}{5})^x=1;x=0$