已知:a+b=7,ab=12,求(a-b)²的值

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已知:a+b=7,ab=12,求(a-b)²的值
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已知:a+b=7,ab=12,求(a-b)²的值
已知:a+b=7,ab=12,求(a-b)²的值

已知:a+b=7,ab=12,求(a-b)²的值
(a-b)²
=a²-2ab+b²
=a²+2ab+b²-4ab
=(a+b)²-4ab
=7²-4x12
=49-48
=1
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因为a+b=7
所以(a+b)^2=7^2
a^2+2ab+b^2=49
a^2+b^2=49-2ab=49-2*12=25

(a-b)^2
=a^2-2ab+b^2
=a^2+b^2-2ab
=25-2*12
=1

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满意请采纳
谢谢

(a-b)²=a²-2ab+b²
a+b=7 (a+b)²=7²=49
a²+2ab+b²=49 a²+b²=49-2*12=25
(a-b)²=a²-2ab+b²=25-2*12=1

(a-b)²=a^2-2ab+b^2=(a+b)²-4ab=7^2-4*12=1

(a+b)^2=49
a^2+b^2+2ab=49
a^2+b^2=49-2ab=25
a^2-2ab+b^2=25-2ab=1
(a-b)^2=1