Question

If the number p is 7 more than the number q and the sum of the squares of p and q is 85,find the product of p and q .
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Answer 1

Answer:

If p is 7 more than q

p = q + 7

the sum of the squares of p and q is 85

p^2 + q^2 = 85

Substitute q + 7 for 'p'

(q + 7)^2 + q^2 = 85

Multiply out

q^2 + 14q + 49 + q^2 = 85

Collect like terms

q^2 + q^2 + 14q + 49 - 85 = 0

2q^2 + 14q - 36 = 0

Divide thro'out by 2

q^2 + 7q - 18 = 0

Factorise

(q - 2)(q + 9) = 0

So, either;

q - 2 = 0

q = 2

OR

q + 9 = 0

q = -9

........

Using q = 2

p = q + 7

p = 9

pq = 9 x 2

pq = 18

........

Using q = -9

p = q + 7

p = -2

pq = 9 x -2

pq = -18

.........

Answer 2

Step-by-step explanation:

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