Question

Решите уравнение по братски

Answer 1

$2*25^{x}-5*4^{x}-3*10^{x}=0\\\\2*\frac{25^{x} }{4^{x} }-5*\frac{4^{x} }{4^{x} }-3*\frac{10^{x} }{4^{x} }=0\\\\2*(\frac{5}{2})^{2x}-3*(\frac{5}{2})^{x}-5=0\\\\(\frac{5}{2})^{x}=m,m>0\\\\2m^{2}-3m-5=0\\\\D=(-3)^{2}-4*2*(-5)=9+40=49=7^{2}\\\\m_{1}=\frac{3+7}{4}=\frac{5}{2}\\\\m_{2} =\frac{3-7}{4}=-1<0\\\\(\frac{5}{2})^{x} =\frac{5}{2}\\\\x=1$