如上题已知a+b=6,ab=4,求(a-b)²的值,我求教懂我,

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如上题已知a+b=6,ab=4,求(a-b)²的值,我求教懂我,如上题已知a+b=6,ab=4,求(a-b)²的值,我求教懂我,如上题已知a+b=6,ab=4,求(a-b)

如上题已知a+b=6,ab=4,求(a-b)²的值,我求教懂我,
如上题已知a+b=6,ab=4,求(a-b)²的值,我求教懂我,

如上题已知a+b=6,ab=4,求(a-b)²的值,我求教懂我,
答:
a+b=6,ab=4
(a-b)²=(a+b)²-4ab
=6²-4*4
=36-16
=20
所以:(a-b)²=20


(a-b)²
=(a+b)²-4ab
=6²-4×4
=36-16
=20

(a-b)^2=(a+b)^2-4ab=6^2-16=36-16=20

(a-b)²=a²-2ab+b²=(a+b)²-4ab=6²-4×4=20

a+b=6,则
(a+b)²=a²+2ab+b²=36
a²+b²=36-2*4=28
(a-b)²=a²-2ab+b²=28-2*4=20

(a+b)²=36=a²+2ab+b²=36,ab=4
a^2+b^2=36-8
a^2+b^2=28
(a-b)²=a²-2ab+b²=28-2*4=28-8=20

a+b=6
两边平方得:a²+2ab+b²=36
那么,a²+b²=36-2ab=36-2×4=28
所以,(a-b)²=a²+b²-2ab=28-2×4=20