If p +5q =28 and $p^{2} + 25 q^{2} = 634$ , then evaluate pq.

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Solution

p+5q =28
$(p + 5 q)^{2} = 28^{2} p^{2} + 10 p q + 25 q^{2} = 784 p^{2} + 5 q^{2} + 10 p q = 784$
634+10 pq =784
10pq =784-634
10pq =150
$p q = \frac{150}{10} = 15$

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