Question

x+y=5 xy=3 (x的五次方+y)+(x+y五次方)

Answer 1

x+y=5,xy=3
则(x+y)²=25
x²+y²=25-2xy=19
x³+y³=(x+y)(x²-xy+y²)
=5[(x+y)²-3xy]
=5×(25-9)
=80
x的五次方+y的五次方
=(x²+y²)(x³+y³)-x²y³-x³y²
=19×80-(xy)²(x+y)
=19×80-9X5
=1475

(x的五次方+y)+(x+y五次方）=1475+5=1480

Answer 2

(x的五次方+y)+(x+y五次方)
= (x^5+y^5)+(x+y)
=(x^4+y^4)(x+y)-x^4y-xy^4+5
=(x^4+y^4)(x+y)-xy(x^3+y^3)+5
=5(x^4+y^4)-3(x^3+y^3)+5
=5[(x^2+y^2)^2-2x^2y^2]-3(x+y)(x^2-xy+y^2)+5
=5[(x^2+y^2)^2-2*9]-3*5*(x^2-3+y^2)+5
=5[19^2-2*9]-3*5*(19-3)+5
=1480
【x^2+y^2=(x+y)^2-2xy=25-6=19】