4x^2+4/x^2+12x+12/x=47

Question

4x^2+4/x^2+12x+12/x=47

Answer 1

4x^2+12x+12/x+4/x^2=47
4(x^2+1/x^2)+12(x+1/x)=47
Пусть x+1/x=t, t^2-2=x^2+1/x^2
4(t^2-2)+12t-47=0
4t^2+12t-55=0
D=1024
t1=(-12-32)/8=-11/2
t2=(-12+32)/8=5/2
1) x+1/x=-11/2
2x^2+11x+2=0
2) x+1/x=5/2
2x^2-5x+2=0