Question

(x^2-5)/x+x/(x^2-5) =17/4

Answer 1

(х²-5)/x=t
t+1/t=17/4
4t²-17t+4=0
D=289-64=225
t1=(17-15)/8=1/4⇒(x²-5)/x=1/4
4x²-x-20=0
D=1+320=321
x1=(1-√321)/8 U x2=(1+√321)/8
t2=(17+15)/8=4²-5)/x=4
x²-4x-5=0
x1+x2=4 U x1*x2=-5⇒x1=-1 U x2=5