Question

If $a+b-12=0$ and $ab=27$, then find the value of $a^3+b^3$.

Answer 1

Compute the required value

Given, $a+b-12=0$

$\Rightarrow a+b=12$

and $ab=27$

We know,

$\begin{array}{ccc}& {\left(a+b\right)}^3=a^3+b^3+3ab(a+b)& \\ \Rightarrow & {\left(12\right)}^3=a^3+b^3+3\times 27\times \left(12\right)& \left[\because a+b=12,ab=27\right]\\ \Rightarrow & a^3+b^3=1728-972& \\ \Rightarrow & a^3+b^3=756& \end{array}$

Therefore, the value of $a^3+b^3=756$.