已知(m-n)^2=8,(m+n)^2=2,则=M^2+n^2=________.

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已知(m-n)^2=8,(m+n)^2=2,则=M^2+n^2=________.
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已知(m-n)^2=8,(m+n)^2=2,则=M^2+n^2=________.
已知(m-n)^2=8,(m+n)^2=2,则=M^2+n^2=________.

已知(m-n)^2=8,(m+n)^2=2,则=M^2+n^2=________.
(m-n)^2=8
m²+n²-2mn=8 (1)
(m+n)^2=2,
m²+n²+2mn=2 (2)
(1)+(2)得:
2(m²+n²)=10
m²+n²=5

(m+n)^2-(m+n)^2=4mn=-6 2mn=-3
M^2+n^2 =(m+n)^2-2mn=5 或直接加起来除以二