已知实数mn满足m+1/2的绝对值与n^2-n+1/4互为相反数,化简并求值：（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2

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已知实数mn满足m+1/2的绝对值与n^2-n+1/4互为相反数,化简并求值：（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2
已知实数mn满足m+1/2的绝对值与n^2-n+1/4互为相反数,化简并求值：（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2

已知实数mn满足m+1/2的绝对值与n^2-n+1/4互为相反数,化简并求值：（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2
∵m+1/2的绝对值非负数,n^2-n+1/4=（n-1/2)^2也非负数
又：m+1/2的绝对值与n^2-n+1/4互为相反数
∴m+1/2的绝对值=0,n^2-n+1/4=（n-1/2)^2=0
∴m=-1/2,n=1/2
∴m+n=0
（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2
= (3m-2n)(3m-2n+3m+2n)-9(m+n)^2
= 6m(3m-2n)-9(m+n)^2
= 6*(-1/2)*{3*(-1/2)-2*1/2}-9*0
= -3*(-5/2)-0
= 15/2

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m+1/2的绝对值与n^2-n+1/4互为相反数，则|m+1/2|+n²-n+1/4=0，则|m+1/2|+(n-1/2)²=0
则m+1/2=0,n-1/2=0，则m=-1/2，n=1/2
（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2
=(3m-2n)(3m-2n+3m+2n)-9(m+n)²
=(3m-2n)*6m-9(m²+2mn+n²)
=18m²-12mn-9m²-18mn-9n²
=9m²-30mn-9n²
=9*1/4+30*1/2*1/2-9*1/4
=30*1/2*1/2
=15/2

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∵m+1/2的绝对值非负数，n^2-n+1/4=（n-1/2)^2也非负数
又：m+1/2的绝对值与n^2-n+1/4互为相反数
∴m+1/2的绝对值=0，n^2-n+1/4=（n-1/2)^2=0
∴m=-1/2，n=1/2
∴m+n=0
（3m-2n）^2+(3m+2n)(3m-2n)-9(m+n)^2
= (3m-2n)(3m-2n+3m+2n...

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