Question
If $p + q = 8$ and $p - q = 4$, find:$pq$
✓
Answer
$(p + q)^2 = (8)^2$
$p^2 + q^2 + 2pq = 64 \dots...(i)$
$(p - q)^2 = (4)^2$
$p^2 + q^2 - 2pq = 16$
$p^2 + q^2 = 16 + 2pq \dots...(ii)$
Using $(ii)$ in $(i)$, we get :
$16 + 2pq + 2pq = 64$
$\Rightarrow 4pq$
$= 64 - 16$
$= 48$
$\Rightarrow pq = 12.$
$p^2 + q^2 + 2pq = 64 \dots...(i)$
$(p - q)^2 = (4)^2$
$p^2 + q^2 - 2pq = 16$
$p^2 + q^2 = 16 + 2pq \dots...(ii)$
Using $(ii)$ in $(i)$, we get :
$16 + 2pq + 2pq = 64$
$\Rightarrow 4pq$
$= 64 - 16$
$= 48$
$\Rightarrow pq = 12.$
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