已知(x+y)²=7,(x-y)²=5,则x²+y²= xy=
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已知(x+y)²=7,(x-y)²=5,则x²+y²= xy=
已知(x+y)²=7,(x-y)²=5,则x²+y²= xy=
已知(x+y)²=7,(x-y)²=5,则x²+y²= xy=
(x+y)²=7
x²+y²+2xy=7 (1)
(x-y)²=5
x²+y²-2xy=5 (2)
(1)+(2)式得:
2x²+2y²=12
x²+y²=6
(1)-(2)式得:
4xy=2
xy=1/2
题错了吧,x²+y²=xy=?????
应该是 x²+y²+xy=? 或 x²+y²-xy=?
当第一种时,=x²+y²+xy+xy-xy
=(x+y)²-xy
∵(x+y)²=7,(x-y)²=5
分解后可得xy=1/2
所以原式=13/2,当第二种时,原式等于11/2
∵( x+y )² = 7
∴ x²﹢y²+2xy =7
∵ ( x-y )² = 5
∴ x² + y²﹣2xy = 5
x²﹢y²+2xy-x² + y²﹣2xy = 2
4xy = 2
xy = 1/2