請問一下，已知x^2+y^2=74，x-y=2，則: (1)x*y=? (2)x+y=? 可以的話請列計算過程，謝謝!?
回答 (3)
2017-09-14 12:07 am
✔ 最佳答案
x^2 + y^2 = 74 .......... (1)x - y = 2 .......... (2)
From (2)
x - y = 2
(x - y)^2 = 4
x^2 - 2xy + y^2 = 4
x^2 + y^2 -2xy = 4
74 - 2xy = 4
-2xy = -70
xy = 35
From (1) , Since
x^2 + y^2 = 74
x^2 + 2xy + y^2 = 74 + 2xy
(x + y)^2 = 74 + 2(35)
(x + y)^2 = 144
x + y = 12 or x + y = -12
2017-09-14 7:00 pm
(x-y)^2+2xy=74
(2)^2+2xy=74
xy=35
(x+y)^2-2xy=74
(x+y)^2=74+70
x+y=+/-12
(2)^2+2xy=74
xy=35
(x+y)^2-2xy=74
(x+y)^2=74+70
x+y=+/-12
2017-09-14 6:19 am
Sol
(1)
設 x+y=2a
x=a+1，y=a－1
x^2+y^2=74
(a+1)^2+(a－1)^2=74
2a^2+2=74
a^2=36
xy=a^2－1=35
(2)
x+y=2a=+/-12
(1)
設 x+y=2a
x=a+1，y=a－1
x^2+y^2=74
(a+1)^2+(a－1)^2=74
2a^2+2=74
a^2=36
xy=a^2－1=35
(2)
x+y=2a=+/-12
收錄日期: 2021-04-24 00:42:24
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170913120320AAVbFKc