Question

已知（x+y)²=9，（x-y)²=1，求值：①x²+y² ②xy ③x^4+y^4

用初三的知识点回答，急急急急。

Answer 1

∵(x+y)²=9
∴x²+2xy+y²=9…………①
∵(x-y)²=1
∴x²-2xy+y²=1…………②

一、
①+②得：
2(x²+y²)=10
x²+y²=5
二、
①-②得：
4xy=8
xy=4
三、
x^4+y^4
=(x²+y²)²-2x²y²
=5²-2*4
=25-8
=17

Answer 2

1=5,
2=2,
3：先分解x^4+y^4
=x^4+2x^2y^2+y^4 -2x^2y^2
=(x^2+y^2)^2-(√2xy)^2
=(x^2+y^2+√2xy)(x^2+y^2-√2xy)
=17

Answer 3

1

Answer 4

1、x^2+y^2
=[(x+y)^2+(x-y)^2]/2
=[9+1]/2
=5
2、xy
=[(x+y)^2-(x-y)^2]/4
=[9-1]/4
=2
3、x^4+y^4
=(x^2+y^2)^2-2(xy)^2
=5^2-2*2^2
=25-8
=17