Question

已知x+y=5，xy=3。求： ①x²+y²；②（x-y）²

回答并有过程，尽量解释清楚，O(∩_∩)O谢谢。

Answer 1

x^2+y^2=(x+y)^2-2xy=5^2-2*3=25-6=19 (x-y)^2=(x+y)^2-4xy=5^2-3*4=25-12=13

Answer 2

x+y=5
(x+y)²=25
x²+2xy+y²=25
x²+y²+2×3=25
x²+y² = 19

（x-y）²
=x²+y²-2xy
=19-2×3
=13

Answer 3

x²+y²
=x²+y²+2xy-2xy
=(x+y)²-2xy
=5²-2×3
=25-6
=19

(x-y)²
=x²+y²-2xy
=19-2×3
=19-6
=13

追问

下一题：已知（a+b）²=30,(a-b)²=20
①求a²+b²的值；②求ab的值

追答

(a+b)²-(a-b)²
=30-20
=10

(a+b)²-(a-b)²
=a²+2ab+b²-a²+2ab-b²
=4ab

4ab=10
ab=2.5

a²+b²
=a²+b²+2ab-2ab
=(a+b)²-2ab
=30-2×2.5
=30-5
=25

Answer 4

x+y=5得x²+y²+2xy=25 xy=3 x²+y²=19
（x-y）²=x²+y²-2xy=（x+y）²-4xy=25-24=1