Question

If a + b = 10 and ab = 21 then $a^3+b^3=$

• A. 270
• B. 370
• C. 470
• D. 170

Answer 1

The correct option is B 370

Given that, $a+b=10$ and $ab=21$

To find out: The value of $a^3+b^3$

We know that, $a^3+b^3=(a+b)(a^2+b^2-ab)$

We can write $(a^2+b^2-ab)$ as $\left[\right(a+b{)}^2-3ab]$

Hence, $a^3+b^3=(a+b)\left[\right(a+b{)}^2-3ab]$

Here, $a+b=10$ and $ab=21$

$\therefore a^3+b^3=\left(10\right)\left[\right(10{)}^2-3\left(21\right)]$

$\Rightarrow a^3+b^3=\left(10\right)[100-63]$

$\therefore a^3+b^3=10\times 37=370$.

Hence, if $a+b=10$ and $ab=21$, then $a^3+b^3=370$.