請列詳解
已知x²+y²=74, x-y=2, 求下列各式的值:
(1) xy
(2) x+y
(數學math)國二數學求解拜託~~
2015-07-26 7:59 am
回答 (4)
2015-07-26 8:22 am
✔ 最佳答案
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x² + y² = 74 ... ①
x - y = 2 ... ②
(1)
從 ② 可知
(x - y)² = 2²
x² - 2xy + y² = 4
(x² + y²) - 2xy= 4
74 - 2xy= 4
2xy = 74 - 4
2xy = 70
xy = 35
(2)
考慮
(x + y)² = x² + 2xy + y²
(x + y)² = (x² + y²) + 2xy
(x + y)² = 74 + 2(35)
(x + y)² = 74 + 70
(x + y)² = 144
x + y = ±√144
x + y = 12 或 -12
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2015-07-28 2:06 am
已知x²+y²=74, x-y=2, 求下列各式的值:
xy
(2) x+y
x^2=x²
(1). (x-y)^2=x²+y²-2xy
=> 2^2=74-2xy
=> 4=74-2xy
=> 2xy=70
=> xy=35
(2). (x+y)^2=x²+y²+2xy
=> (x+y)^2=74+2*35
=> (x+y)^2=144
=> x+y=12
xy
(2) x+y
x^2=x²
(1). (x-y)^2=x²+y²-2xy
=> 2^2=74-2xy
=> 4=74-2xy
=> 2xy=70
=> xy=35
(2). (x+y)^2=x²+y²+2xy
=> (x+y)^2=74+2*35
=> (x+y)^2=144
=> x+y=12
2015-07-26 8:28 am
x-y=2
x=2+y.....代 入x^2+y^2=74
(2+y)^2+y^2=74
4+4y+y^2+y^2=74
2y^+4y-70=0(各項處以2)
y^2+2y-35=0
(y+7)*(y-5)=0
y=-7or5(代 入x-y=2)
x=-5 or7
xy=35
x+y=-12 or12
x=2+y.....代 入x^2+y^2=74
(2+y)^2+y^2=74
4+4y+y^2+y^2=74
2y^+4y-70=0(各項處以2)
y^2+2y-35=0
(y+7)*(y-5)=0
y=-7or5(代 入x-y=2)
x=-5 or7
xy=35
x+y=-12 or12
收錄日期: 2021-05-01 19:27:41
原文連結 [永久失效]:
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