If a+b=12 and ab=27, find the value of a3+b3.

# If $a+b=12$ and $\mathit{ab}=27$, find the value of ${a}^{3}+{b}^{3}.$

1. A
$752$
2. B
$756$
3. C
$753$
4. D
$754$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

It is given that $a+b=12$ and $\mathit{ab}=27$
We have to find the value of ${a}^{3}+{b}^{3}$.
We know the algebraic identity, ${\left(a+b\right)}^{3}={a}^{3}+{b}^{3}+3\mathit{ab}\left(a+b\right)$ .
Put the value of $a+b=12$ in above identity, we get,
${\left(12\right)}^{3}={a}^{3}+{b}^{3}+3\mathit{ab}\left(12\right)$ ${\left(12\right)}^{3}={a}^{3}+{b}^{3}+3\left(27\right)\left(12\right)$
$12×12×12={a}^{3}+{b}^{3}+3\left(27\right)\left(12\right)$
$1728={a}^{3}+{b}^{3}+972$
${a}^{3}+{b}^{3}=1728-972$
${a}^{3}+{b}^{3}=756$
Therefore, option 2 is  correct.

## Related content

 Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)