Question

If $a+b=30$ and $ab=176$, find $a^3+b^3$

• A. $10160$
• B. $11060$
• C. $11160$
• D. $Noneofthese$

Answer 1

The correct option is C $11160$

$a+b=30,ab=176a+b=30\Rightarrow {\left(a+b\right)}^2={\left(30\right)}^2$

$\Rightarrow a^2+b^2+2ab=900\Rightarrow a^2+b^2+2\times 176=900\Rightarrow a^2+b^2=900-352\Rightarrow a^2+b^2=548$

$Now{a}^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right)=30\left(548-176\right)=30\times 372=11160$