Question

If $pq=3$, then $p^3{q}^4+p^4{q}^5=$

• A. $12q$
• B. $7p+9q$
• C. $12p+20q$
• D. $96p$
• E. $108q$

Answer 1

Answer: (E)

$108q$

Given, $pq=3$
To find $p^3{q}^4+p^4{q}^5$
$\Rightarrow pq=3$
$\Rightarrow p=\frac{3}{q}$
$\therefore p^3{q}^4+p^4{q}^5$
$={\left(\frac{3}{q}\right)}^3{q}^4+{\left(\frac{3}{q}\right)}^4{q}^5$ .....(putting the value $p=\frac{3}{q})$
$=\left(\frac{27}{q^3}\right)q^4+\left(\frac{81}{q^4}\right)q^5$
$=27q+81q$
$=108q$