已知m+n=2/p mn=-1 1/n-1/m=4/p的绝对值 则p值为（ ）
问答/446℃/2024-06-30 18:01:27
优质解答：
m + n = 2/p ………………………………………①
mn = -1 ……………………………………………②
1/n - 1/m =│4/p│………………………………③
由①得(m+n)^2 = 4/p^2
m^2 + 2mn + n^2 = 4/p^2
将②代入上式得m^2 + n^2 = 4/p^2 + 2………④
③式可变形为(m - n)/mn =│4/p│
即(m - n)^2/(mn)^2 = 16/p^2
(m^2 + n^2 - 2mn)/(mn)^2 = 16/p^2
将②④代入上式得(4/p^2 + 2 + 2)/(-1)^2 = 16/p^2
解上式得p^2 = 3
p = ±根3