已知m=99又1/2,n=50又1/4,求代数式(2m-n)^2-(3m-n)(m-n)-4n^2的值

问题描述:

已知m=99又1/2,n=50又1/4,求代数式(2m-n)^2-(3m-n)(m-n)-4n^2的值

∵m=99又1/2=199/2,n=50又1/4=201/4
∴(2m-n)²-(3m-n)(m-n)-4n²=4m²-4mn+n²-3m²+4mn-n²-4n²
=4m²-4n²=4(m+n)(m-n)=4×(199/2+201/4)(199/2-201/4)
=4×599/4×197/4=29500又3/4


(2m-n)^2-(3m-n)(m-n)-4n^2
=(4m^2-4mn+n^2)-(3m^2-4mn+n^2)-4n^2
=4m^2-4mn+n^2-3m^2+4mn-n^2-4n^2
=m^2-4n^2
=(m+2n)(m-2n)
=200*(-4)
=-800