Question

Find the value of $a$ and $c$, if
$\left(i\right)8a={35}^2-{27}^2$

$\left(ii\right)p{q}^{2}c=(4pq+3q{)}^2-(4pq-3q{)}^2$

• A. a=62 , c=48
• B. a=60 , c=48
• C. a=62 , c=46
• D. a=62 , c=38

Answer 1

The correct option is A $(a=62,c=48)$

(i) Given equation $8a={35}^2-{27}^2$
Use the formula of $a^2-b^2=(a-b)(a+b)$
$\Rightarrow (35-27)(35+27)=8\times 62$
Thus, given expression is $8a=8\times 62$
$\therefore a=62$

(ii)Given equation $p{q}^{2}c=(4pq+3q{)}^2-(4pq-3q{)}^2$
$=(4pq+3q+4pq-3q)(4pq+3q-4pq+3q)$ [Since, $(a+b{)}^2=a^2+2ab+b^2$]
$\Rightarrow p{q}^{2}c=8pq\times 6q$
$\Rightarrow p{q}^{2}c=48p{q}^2$
$\therefore c=48$