如图已知实数m,n满足(m=n)2=1,(m-n)2=25,求m2+mn+n2的值
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如图已知实数m,n满足(m=n)2=1,(m-n)2=25,求m2+mn+n2的值
如图已知实数m,n满足(m=n)2=1,(m-n)2=25,求m2+mn+n2的值
如图已知实数m,n满足(m=n)2=1,(m-n)2=25,求m2+mn+n2的值
即m²+2mn+n²=1
m²-2mn+n²=25
相减
4mn=-24
mn=-6
m²+2mn+n²=1
两边减去mn
m²+mn+n²
=1-mn
=1-(-6)
=7
(m+n)2=1 m^2+n^2+2mn=1
(m-n)2=25 m^2+n^2-2mn=25
两式相加得
2m^2+2n^2=26
m^2+n^2=13
两式相减得
4mn=-24
mn=-6
m2+mn+n2=13-6=7
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