已知x+y=-3 x^3+y^3=-18 求x^7+y^7的值
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已知x+y=-3 x^3+y^3=-18 求x^7+y^7的值
(x+y)^2=9
x^2+y^2+2xy=9
x^2+y^2=9-2xy
x^3+y^3
=(x+y)(x^2-xy+y^2)
=-3*(9-2xy-xy)=-18
9-3xy=6
xy=1
x^2+y^2=9-2xy=7
(x^2+y^2)^2=x^4+2(xy)^2+y^4=49
x^4+y^4=49-2=47
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=-18*47-x^3y^3(x+y)
=-846+3*(xy)^2
=-843
x^2+y^2+2xy=9
x^2+y^2=9-2xy
x^3+y^3
=(x+y)(x^2-xy+y^2)
=-3*(9-2xy-xy)=-18
9-3xy=6
xy=1
x^2+y^2=9-2xy=7
(x^2+y^2)^2=x^4+2(xy)^2+y^4=49
x^4+y^4=49-2=47
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=-18*47-x^3y^3(x+y)
=-846+3*(xy)^2
=-843
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