Question

已知x+y=7，xy=2，求2x²+2y²的值；求（x-y）²得值。

Answer 1

解：∵x+y=7
∴（x+y）²=49
∴x²+2yx+y²=49
又∵xy=2
∴x²+2×2+y²=49
∴x²+y²=45
2x²+2y²=2（x²+y²）=2×45=90，
（x-y）²=x²-2yx+y²=45-2×2=41

Answer 2

已知x+y=7，xy=2，求2x²+2y²的值；求（x-y）²得值
解：2x2+2y2=2(x2+y2)=2〔(x+y)2-2xy〕=2〔72-2×2〕=90
(x-y)2=x2-2xy+y2= (x2+ y2)-2xy=90/2-2*2=41

Answer 3

x+y=7，
xy=2，
2x²+2y²
=2(x²+y²)
=2[(x+y)²-2xy}
=2[7²-2*2]
=90

(x-y)²=(x+y)²-4xy=7²-4*2=41.

Answer 4

2x²+2y²
=2（X^2+y^2)
=2[(X+y)^2-2xy]
=2*(49-4)
=90

x^2+y^2=45

（x-y）²
=x^2+y^2-2xy
=45-4
=41

Answer 5

2x^2+2y^2
=2(x^2+y^2)
=2[(x+y)^2-2xy]
=2(7^2-2×2)
=2×45
=90

(x-y)^2=(x+y)^2-4xy
=7^2-4×2
=49-8
=41