问一下两道题！~！

显示全部楼层 · 2008-5-28 17:56:33

1.已知x+y=1,x的平方+y的平方=2。那么x的四次方+y的四次方=?
2.已知（x+y)的平方-2x-2y+1=0.则(x+y)的九百九十九次方=?

PS:要有详细过程（和解说）哦！~~

千问 · 2008-5-28 17:56:33

x+y=1两边平方x^2+2xy+y^2=1x^2+y^2=2相减2xy=-1xy=-1/2x^2+y^2=2两边平方x^4+2x^2y^2+y^4=4所以x^2+y^4=4-2x^2y^2=4-2(xy)^2=4-2*1/4=7/2（x+y)^2-2x-2y+1=0.(x+y)^2-2(x+y)+1=0(x+y-1)^2=0x+y-1=0x+y=1(x+y)^999=1

千问 · 2008-5-28 17:56:33

1.已知x+y=1,x的平方+y的平方=2 x^2+y^2=2 x^2+2xy+y^2=2+2xy (x+y)^2=2+2xyxy=-1/2 x^4+x^4=x^2+2xy+y^2+x^2+2xy+y^2-4xy=02.(x+y)^2-2x-2y+1=0 (x+y)^2-2(x+y)+1=0(x+y-1)^2=0