已知实数a,b满足ab=1,a+b=3,求代数式a³b+ab³的值
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已知实数a,b满足ab=1,a+b=3,求代数式a³b+ab³的值
已知实数a,b满足ab=1,a+b=3,求代数式a³b+ab³的值
已知实数a,b满足ab=1,a+b=3,求代数式a³b+ab³的值
a³b+ab³
=ab(a²+b²)
=(a+b)²-2ab
=3²-2
=7
a³b+ab³
=ab(a²+b²)
=ab(a²+b²+2ab-2ab)
=ab[(a+b)²-2ab]
=1×(3²-2×1)
=7
a³b+ab³
=ab(a²+b²)(提公因式)
=ab(a²+b²+2ab-2ab)
=ab[(a+b)²-2ab](完全平方公式)
将ab=1,a+b=3代入上式
原式=1×(3²-2)
=9-2
=7
a³b+ab³
=ab(a^2b+ab^2)
=ab(a^2b+ab^2+2ab-2ab)
=ab[(a+b)^2-2ab]
=1[3^2-2]=7
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