Question

Решите уравнение: 5*2^(2x)-7*10^(x)+2*5^(2x)=0

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Answer 1

фото........................

Answer 2

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