Question

已知x的平方加上y的平方等于6,xy=2,求x的6次加上y的6次的值.

望有详细过程！

Answer 1

由x²+y²=6，xy=2, x²y²=4
∴(x²+y²)²=36

x^4+2x²y²+y^4=36
x^4-x²y²+y^4=36-12=24
x^6+y^6=(x²+y²)(x^4-x²y²+y^4)
=6×24
=144.

Answer 2

x²+y²=6,xy=2
=>(x²+y²)²=36
=>x^4+y^4=32
=>(x²+y²)(x^4+y^4)=192
=>x^6+y^6
=192-[x²y^4+x^4y²]
=192-(xy)²(x²+y²）
=192-4*6
=168

Answer 3

x²+y²=6,xy=2
=>(x²+y²)²=36
=>x^4+y^4=32
=>(x²+y²)(x^4+y^4)=192
=>x^6+y^6
=192-[x²y^4+x^4y²]
=192-(xy)²(x²+y²）
=192-4*6
=168