Question

已知1/p-1/q-1/（p+q）=0,求（q/p+p/q)²的值..

Answer 1

1/p-1/q-1/(p+q)=0

通分整理 (q^2-p^2-pq)/qp(p+q)=0

分母不能为0,所以q^2-p^2-pq=0 pq=q^2-p^2 (1)

(q/p-p/q)^2=[(q^2-p^2)/pq]^2 （通分）(2)

(q/p-p/q)^2=q^2/p^2+p^2/q^2-2 (3)

(1)代入(2) (q/p-p/q)^2=1

(2)代入(3) q^2/p^2+p^2/q^2=3

(q/p+p/q)^2=q^2/p^2+p^2/q^2+2=3+2=5

答案为5