Question

if the number p is 5 more than q and the sum of the squares of of p and q is 55 then the product of p and q is

Answer 1

given p= 5+q
p^2 +q ^2 =55
=> (5+q)^2 +q^2 = 55
25 + q^2 + 10q + q^2 =55
2q^2 +10q - 30 =0
q^2 +5q -15 =0 [ dividing each term by 2]
=>5q+q^2=15
product of p and q = pq = (5+q)q [As p = 5+q]
=>pq= 5q+q^2
=> pq = 15 [ as we have found that 5q+q^2 = 15]

Answer 2

Let q = p+5
(p)²+(p+5)²= 55
2p²+10p+25 = 55
2p²+10p = 30

Dividing by two on both sides,
 p² + 5p = 15
p(p+5) = 15

Since, p(p+5) is the product of p and q,
Therefore, the answer is 15.

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