已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4
问题描述:
已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4
答
已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4
x^2+y^2=(x+y)^2-2XY=9*9-2*10=61
x^3+y^3=(x+y)^3-3xy(x+y)=729-3*10*9=529
x^4+y^4=(x^2+y^2)^2-2x^2y^2=61*61-2*10*10=3721-200=3521