Question

Cho \(a+b=p,a-b=q\) tính \(a.b,a^3+b^3\)

3 tick giúp tớ.

Answer 1

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

\(\Rightarrow a^2-2ab+b^2+4ab=p^2\)

\(\Rightarrow\left(a-b\right)^2+4ab=p^2\)

\(\Rightarrow q^2+4ab=p^2\Rightarrow ab=\frac{p^2-q^2}{4}\)

\(a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)=\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\)

\(=p\left(q^2+\frac{p^2-q^2}{4}\right)=\frac{p\left(3q^2+p^2\right)}{4}\)