Question

If $2p=3q+\sqrt{5p^2-m}$, express m in terms of p and q.

• A. $m=9p^2-q^2+3pq$
• B. $m=p^2-3q^2+4pq$
• C. $m=p^2-9q^2+12pq$
• D. $m=9p^2-3q^2+pq$

Answer 1

The correct option is C $m=p^2-9q^2+12pq$

Given, $2p=3q+\sqrt{5p^2-m}$

$2p-3q=\sqrt{5p^2-m}$

Squaring on both sides, we get
${(2p-3q)}^2=5p^2-m$
$4p^2-12pq+9q^2=5p^2-m$
$\therefore m=5p^2-4p^2+12pq-9q^2$

$=p^2+12pq-9q^2$