1,已知1/x + 1/y = 1/(x+y)

问题描述:

1,已知1/x + 1/y = 1/(x+y)
则 y/x + x/y = _________
2,已知a + 1/a = 7
则 a - 1/a = ______________

(2表示平方)
y/x+x/y=(x2+y2)/xy=(x2+2乘以xy+y2)/xy-(2乘以xy)/xy=((x+y)2)/xy-2
因为1/y+1/x=1/(x+y)化简成(x+y)2=xy
带入,答案为-1
(a+1)/a=1+(1/a)=7推出(1/a)=6
(a-1)/a=1-(1/a)=-5