Question

已知x+y=10.xy=24.求x^3+y^3,x^4+y^4

Answer 1

∵x+y=10, ∴(x+y)^2=100

∴x^2+2xy+y^2=100

∴x^2+y^2=100-2xy=100-2*24=52

∴x^3+y^3=(x+y)(x^2-xy+y^2)=10*(52-24)=280

x^4+y^4=(x^2+y^2)-2x^2*y^2=52^2-2*24^2=1552

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