已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值

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已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值

已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值
已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值

已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值
4m+n=90
2m-3n=10 得:-(2m+3n)=-10
(m+2n)^2-(3m-n)^2
=[(m+2n)+(3m-n)][(m+2n)-(3m-n)]
=(4m+n)(-2m+3n)
=90x(-10)
=-900

(M+2N)^2-(3M-N)^2
=[(m+2n)+(3m-n)][(m+2n)-(3m-n)]
=(4m+n)(-2m+3n)
=-(4m+n)(2m-3n)
=-90*10
=-900.

(M+2N)^2-(3M-N)^2
=[(m+2n)+(3m-n)][(m+2n)-(3m-n)]
=(4m+n)(-2m+3n)
=-(4m+n)(2m-3n)
=-90*10
=-900.

(m+2n)^2-(3m-n)^2=(m+2n+3m-n)(m+2n-3m+n)=(4m+n)(-2m+3n)=90×(-10)=-900

4m+n=90,2m-3n=10
n=10 m=20
(m+2n)^2-(3m-n)^2
=(20+10)^2-(3X20-10)^2
=900-250
=650

4m+n=90 1式
2m-3m=10 2式
由1、2可得n=10,m=20,
代入式子就可以了