Question

Решите уравнение:)

5х^-2 +7х^-1 +2=0​

Answer 1

$5x^{-2}+7x^{-1}+2=0$

Сделаем замену :

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