Question

Решите уравнение x^-4+81=18x^-2

Answer 1

$x^{-4}+81=18x^{-2}\ \ frac{1}{x^4}+81=frac{18}{x^2}\ \ frac{1}{x^4}-frac{18}{x^2}+81=0\ \ frac{1-18x^2}{x^4}=-81\ 1-18x^2=-81x^4\ 81x^4-18x^2+1=0\ \ \ x^2=t\ \ 81t^2-18t+1=0\ (9t-1)^2=0\ 9t-1=0\ 9t=1\ t=frac{1}{9} => x= ^+_-frac{1}{3}$