已知(m-n)²=8,(m+n)²=2,求m²+n²及m·n的值
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已知(m-n)²=8,(m+n)²=2,求m²+n²及m·n的值
已知(m-n)²=8,(m+n)²=2,求m²+n²及m·n的值
已知(m-n)²=8,(m+n)²=2,求m²+n²及m·n的值
(m-n)²=8
m²+n²-2mn=8 (1)
(m+n)²=2
m²+n²+2mn=2 (2)
(1)+(2)式得:
2m²+2n²=10
m²+n²=5
(2)-(1)式得:
4mn=-6
mn=-3/2
∵(m-n)²=8,(m+n)²=2
∴m²-2mn+n²=8 m²+2mn+n²=2
2m²+2n²=10 4mn=-6
∴m²+n²=5 mn=-1.5