Question

11•9^х-7•15^х-4•25^х=0

Answer 1

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