Question

There are two numbers such that sum of the numbers is 14 and the sum of their squares is 106. Find their product.​

Answer 1

Step-by-step explanation:

Let the numbers be a and b

ab = 45 …(1)

a-b = 4, or a = 4+b …(2)

Put (1) in (2)

b(4+b) = 45

b^2+4b=45 = 0

(b+9)(b-5) = 0

Hence b = 5 or -9 and the corresponding value of a = 9 or -5.

The sum of the squares of a and b = 25+81 = 106.