已知ab=12,求2a²+2b²的最小值
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已知:a+b=8,ab=-12,求a²+b²的值.a²+b²=(a+b)²-2ab=64-24=40.
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ab(a^2b^5-ab^3-b)=a^3b^6-a^2b^4-ab^2=(ab^2)^3-(ab^2)^2-ab^2=6³-6²-6=216-36-6=174
a+2b=0a=-2ba²=4b²∴a²+2ab-b²=4b²-4b²-b²=-b²2a²+ab+b²
(3a-4b-ab)-(a-2b+3ab)=3a-4b-ab-a+2b-3ab=2a-2b-4ab=2(a-b)-4ab=2×(-1)-4×(-2)(将a-b=-1,ab=-2代入)=-2+8=6
ab^2=-2-ab(a^2b^5-ab^3-b)=-a^3b^6+a^2b^4+ab^2=-(ab^2)^3+(ab^2)^2+ab^2=-(-2)^3+(-2)^2+(-2)=8+4-2=10
ab^2=-6所以-ab(a^2*b^5-ab^3-b)=-a^3b^6+a^2b^4+ab^2=-(ab^2)^3+(ab^2)^2+(ab^2)=-(-6)^3+(-6)^2+(-6)=216+3
ab(36b-6b-b)=29ab^2=(30-1)*6=174
ab(ab^3+a^2b^5-b)=ab²(ab²+a²b^4-1)=6*(6+6²-1)=6*41=246
a^2b-ab^2=ab(a-b)把a-b=1,ab=12代入ab(a-b)=12
a-b=3ab2a-2b-ab/a-b+2ab=6ab-ab/3ab+2ab=5ab/5ab=1
a^2-ab=17ab-b^2=12这2个等式的左边和左边相加,右边与右边相加,得到a^2-ab+ab-b^2=a^2-b^2=29
12a-12ab+3b=3(4a-4ab+b)=3(2a-b)=3*(1/3)=3*1/9=1/3
2a+2b-ab分之a+b+2ab=2(a+b)-ab分之a+b+2ab=6ab-ab分之3ab+2ab=5ab分之5ab=1
(a+b)(a-b)=12设x=a+b,y=a-b,则a=(x+y)/2,b=(x-y)/2,xy=12a^2+b^2+ab=(x+y)²/4+(x-y)²/4+(x+y)(x-y
a-b-3ab=0a-b=3ab(2a+3ab-2b)/(a-ab-b)=[2(a-b)+3ab]/(a-b-ab)=9ab/2ab=9/2
a-ab=26变形得:a=26+ab.ab-b=-18变形得:b=18+ab所以a-b=ab+26-18-ab=8a-2ab+b=26+ab+18+ab-2ab=44满意请采纳
ab/a+b=3ab=3(a+b)2ab/a+b-5(a+b)/ab=6(a+b)/(a+b)-5(a+b)/3(a+b)=6-5/3=13/3
ab/(a+b)=3,a+b=ab/3原式=[3(a+b)+ab]/[2(a+b)-ab]=[3(ab/3)+ab]/[2(ab/3)-ab]=2ab/(-ab/3)=-6