Question

Cho a+b = 5

ab=6

Không tính a;b hãy tính a⁵+b⁵

Answer 1

Ta có:

+) \(a+b=5\)

\(\Rightarrow\left(a+b\right)^2=25\)

\(\Rightarrow a^2+b^2+2ab=25\)

\(\Rightarrow a^2+b^2=13\)

+) \(a+b=5\)

\(\Rightarrow\left(a+b\right)^3=125\)

\(\Rightarrow a^3+3ab\left(a+b\right)+b^3=125\)

\(\Rightarrow a^3+b^3=35\)

+) \(\left(a^2+b^2\right)\left(a^3+b^3\right)=13.35\)

\(\Rightarrow a^5+a^2b^3+b^2a^3+b^5=455\)

\(\Rightarrow a^5+b^5+a^2b^2\left(a+b\right)=455\)

\(\Rightarrow a^5+b^5=275\)

Vậy...