已知x+y=6且xy=4 求 :(1)x2+y2 (2) (x-y)2 (3) x的四次方+y的四次方

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已知x+y=6且xy=4求:(1)x2+y2(2)(x-y)2(3)x的四次方+y的四次方已知x+y=6且xy=4求:(1)x2+y2(2)(x-y)2(3)x的四次方+y的四次方已知x+y=6且xy

已知x+y=6且xy=4 求 :(1)x2+y2 (2) (x-y)2 (3) x的四次方+y的四次方
已知x+y=6且xy=4 求 :(1)x2+y2 (2) (x-y)2 (3) x的四次方+y的四次方

已知x+y=6且xy=4 求 :(1)x2+y2 (2) (x-y)2 (3) x的四次方+y的四次方
1.x2+y2=(x+y)2-2xy=36-8=28
2.(x-y)2=(x+y)2-4xy=36-16=20
3.x4+y4=(x2+y2)2-2(xy)2=784-32=752

1.x2+y2=(x+y)2-2xy=36-8=28
2.(x-y)2=(x+y)2-4xy=36-16=20
3.x4+y4=(x2+y2)2-2(xy)2=784-32=752

(1)x2+y2=(x+y)2-2xy=28
(2)(x-y)2=(x+y)2-4xy=20
(3)x4+y4=x4+2x2y2+y4-2x2y2=(x2+y2)2-2x2y2=752