Question

(x^2 + 16/x^2)-(x+4/x)-12=0

Answer 1

x+4/x=y
x²+16/x²+8=y²⇒x²+16/x²=y²-8
y²-8-y-12=0
y²-y-20=0⇒y1=5; y2=-4
x+4/x=5⇒x²-5x+4=0⇒x1=1; x2=4
x+4/x=-4⇒x²+4x+4=0⇒x=-2