Question

[Đỗ Quyết]

X+y=5; x^2+y^2=17 . Tính x^5+y^5

Answer 1

[Lấp La Lấp Lánh]

Ta có: \(x+y=5\Rightarrow\left(x+y\right)^2=25\)

\(\Rightarrow x^2+2xy+y^2=25\)

\(\Rightarrow2xy+17=25\)\(\Rightarrow2xy=8\Rightarrow xy=4\)

\(x^5+y^5=\left(x^2+y^2\right)\left(x^3+y^3\right)-x^2y^2\left(x+y\right)=17.\left(x+y\right)\left(x^2-xy+y^2\right)-4^2.5=17.5\left(17-4\right)-80=1025\)

Answer 2

[Đỗ Quyết]

M cảm ơn