化简求值:若4x2+4x+y2-6y+10=0,试求(x2+2y2+3)(x2+2y2-3)-(x-2y)2(x+2y)2的值.
题型:解答题难度:一般来源:不详
化简求值:若4x2+4x+y2-6y+10=0,试求(x2+2y2+3)(x2+2y2-3)-(x-2y)2(x+2y)2的值. |
答案
∵4x2+4x+y2-6y+10=0, ∴4x2+4x+1+y2-6y+9=0, ∴(2x+1)2+(y-3)2=0, ∴2x+1=0,y-3=0, ∴x=-,y=3, ∴原式=(x2+2y2)2-9-(x2-4y2)2 =(x2+2y2+x2-4y2)(x2+2y2-x2+4y2)-9 =6y2×(2x2-2y2)-9 =12y2(x2-y2)-9 =12×9×(-)-9 =-995-9 =-1004. |
举一反三
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下列计算中不正确的是( )A.(-m)(-m)2=m3 | B.(-m)4(-m)2=m6 | C.(-m)3(-m)2=-m5 | D.(-m)3(-m)3=m6 |
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