若实数a,b满足1⼀a-1⼀b-1⼀(a+b)=0,求b^2⼀a^2-a^2⼀b^2的值

2025-02-28 03:12:21
推荐回答(1个)
回答1:

1/a-1/b-1/(a+b)=0有
(b-a)/ab-1/(a+b)=0,
b^2-a^2-ab=0,
(b-a/2)^2=5a^2/4,
b1=a(1+√5)/2,b2=a(1-√5)/2.
(b1/a1)^2=(3+√5)/2,(a1/b1)^2=(3-√5)/2,
(b2/a2)^2=(3-√5)/2,(a2/b2)=(3+√5)/2.
b^2/a^2-a^2/b^2的值为:√5或-√5.