已知a-b=7,ab=2,求a²+b²和a+b²的值已知4x²+y²-4x+10y+26=0,求6x-五分之一y的值.

Question

已知a-b=7,ab=2,求a²+b²和【a+b】²的值
已知4x²+y²-4x+10y+26=0,求6x-五分之一y的值.

Answer 1

a²+b²
= a²+b² -2ab +2ab
= (a-b)²+2ab
= 7²+2×2
= 53
(a+b)²
= a²+b² +2ab
= a²+b² -2ab +4ab
= (a-b)²+4ab
= 7²+4×2
= 57
因为：
4x²+y²-4x+10y+26
= 4x²-4x+1+y²+10y+25
= (2x-1)² +(y+5)²
= 0
所以 2x-1 =0,y+5 =0
得 x = 1/2,y = -5
6x-y/5
= 6×1/2 -(-5)/5
= 3+1
=4
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