若a+b=7,ab=5,则(a-b)²的值

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若a+b=7,ab=5,则(a-b)²的值

若a+b=7,ab=5,则(a-b)²的值
若a+b=7,ab=5,则(a-b)²的值

若a+b=7,ab=5,则(a-b)²的值
(a-b)²
=a^2+b^2-2ab
=a^2+b^2+2ab-4ab
=(a+b)^2-4ab
=49-20
=29

(a-b)²
=a²-2ab+b²
=a²+2ab+b²-4ab
=(a+b)²-4ab
=7²-4×5
=29

展开得a²-2ab+b²=a²+2ab+b²-4ab=(a+b)²-4ab=49-20=29

(a-b)²=(a+b)²-4ab=29

(a-b)²=(a+b)²-4ab=7²-4×5=29
下面两个等式可做为公式用
(a-b)²=(a+b)²-4ab
(a+b)²=(a-b)²+4ab