已知1/a+1/b+1/a+b=0,求(b/a)^2+(a/b)^2的值

1/a+1/b+1/(a+b)=0
(a+b)/(ab)=-1/(a+b)
(a+b)²=-ab
(b/a)²+(a/b)²
=(a⁴+b⁴)/(a²b²)
=[(a²+b²)²-2a²b²]/(a²b²)
=(a²+b²)²/(a²b²) -2
=[(a+b)²-2ab]²/(a²b²) -2
=[-ab-2ab)²/(a²b²) -2
=(-3ab)²/(a²b²) -2
=9a²b²/(a²b²) -2
=9-2
=7