正数ab满足a^3b+ab^3-2a^2b+2ab^2=7ab-8 求a^2-b^2

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正数ab满足a^3b+ab^3-2a^2b+2ab^2=7ab-8求a^2-b^2正数ab满足a^3b+ab^3-2a^2b+2ab^2=7ab-8求a^2-b^2正数ab满足a^3b+ab^3-2a

正数ab满足a^3b+ab^3-2a^2b+2ab^2=7ab-8 求a^2-b^2
正数ab满足a^3b+ab^3-2a^2b+2ab^2=7ab-8 求a^2-b^2

正数ab满足a^3b+ab^3-2a^2b+2ab^2=7ab-8 求a^2-b^2
a^3b+ab^3-2a^2b+2ab^2=7ab-8
ab(a^2+b^2)-2ab(a-b)=7ab-8
ab(a^2-2ab+b^2)-2ab(a-b)=-2a^2b^2+7ab-8
ab[(a-b)^2-a(a-b)+1]=-2(a^2b^2-4ab+4)
ab(a-b-1)^2=-2(ab-2)^2
因为a,b为正数,所以只能两个平方数均为0.
即 a-b-1=0,
ab-2=0,
联立方程解得,
a=2,
b=1.
a^2-b^2=2^2-1^2=4-1=3

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