Question

已知实数x,y满足x+y=1,x的平方+y的平方=2,求x的六次方+y的六次方的值.

Answer 1

x+y=1,x²+y²=2

则：(x+y)²=x²+2xy+y²

1=2+2xy

得：xy=-1/2,则：x²y²=1/4

x^6+y^6=(x²+y²)(x⁴-x²y²+y⁴)

x⁴+y⁴=(x²+y²)²-2x²y²

则：x⁴-x²y²+y⁴=(x²+y²)²-3x²y²=4-3/4=13/4

所以：x^6+y^6=(x²+y²)(x⁴-x²y²+y⁴)=13/2