已知(m+n)^2=7,(m-n)^2=3则m^2+n^2

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已知(m+n)^2=7,(m-n)^2=3则m^2+n^2已知(m+n)^2=7,(m-n)^2=3则m^2+n^2已知(m+n)^2=7,(m-n)^2=3则m^2+n^2(m+n)^2=7m

已知(m+n)^2=7,(m-n)^2=3则m^2+n^2
已知(m+n)^2=7,(m-n)^2=3则m^2+n^2

已知(m+n)^2=7,(m-n)^2=3则m^2+n^2
(m+n)^2=7
m²+2mn+n²=7
,(m-n)^2=3
m²-2mn+n²=3
两个式子相加
2(m²+n²)=10
m²+n²=5

(m+n)^2=m^2+2mn+n^2=7
(m-n)^2=m^2-2mn+n^2=3
两式相减,得 4mn=4,因此 mn=1
m^2+2mn+n^2=7,得 m^2+n^2=7-2=5

已知(m+n)^2=7
m^2+2mn+n^2=7
(m-n)^2=3
m^2-2mn+n^2=3
2(m^2+n^2)=10
m^2+n^2=5