★★★已知x+y=6,xy=4,求x^4+y^4,(x+1)(x-1),x^3+y^3

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★★★已知x+y=6,xy=4,求x^4+y^4,(x+1)(x-1),x^3+y^3
★★★已知x+y=6,xy=4,求x^4+y^4,(x+1)(x-1),x^3+y^3

★★★已知x+y=6,xy=4,求x^4+y^4,(x+1)(x-1),x^3+y^3
x²+y²=(x+y)²-2xy=6²-4*2=28
x^4+y^4=(x²+y²)²-2(xy)²=28²-2×4²=752
y=6-x
xy=x(6-x)=6x-x²=4
x²-6x+4=0
解得x=3±根号5
(x+1)(x-1)
=x²-1
=13±6根号5
x³+y³=(x+y)(x²-xy+y²)=6×(28-4)=144

x2+y2=(x+y)2-2xy=28
x^4+y^4=(x2+y2)2-2(xy)2=784-32=752
x+y=6,xy=4
x+4/x=6
x2-6x+4=0
(x-3)2=5
x=3±√5
(x+1)(x-1)＝x2-1=6x-4-1=6x-5=13±6√5
x^3+y^3=(x+y)^3-3xy(x+y)=216-72=144

因为x+y=6,xy=4
(1)x^4+y^4=(x^2+y^2)^2-2*x^2*y^2=(6^2-2*4)^2-2*4^2=752
(2)有问题,有两个答案13+6根号5 和13-6根号5
(3)x^3+y^3=(x+y)(x^2-xy+y^2)=6*(6^2-4*3)=144

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