Question

помогите пожалуйста...

Answer 1

$5^{\frac{x+4}{x} }-124*5^{\frac{2}{x} } -25=0\\\\ 5^{\frac{x}{x} +\frac{4}{x} } -124*5^{\frac{2}{x} }-25=0\\\\5*5^{\frac{4}{x} }-124*5^{\frac{2}{x} }-25=0$

Сделаем замену :

$5^{\frac{2}{x} }=m,m>0$

Тогда :

$5^{\frac{4}{x} }=(5^{\frac{2}{x} })^{2}=m^{2}$

$5m^{2}-124m-25=0\\\\D=(-124)^{2}-4*5*(-25)=15376+500=15876=126^{2}\\\\m_{1} =\frac{124+126}{10} =\frac{250}{10}=25\\\\m_{2}=\frac{124-126}{10}=-0,2<0\\\\5^{\frac{2}{x} }=25\\\\5^{\frac{2}{x} }=5^{2}\\\\\frac{2}{x}=2\\\\x=1$