The sum of two numbers is 14.And the sum of the squares of these numbers is 100.Find the ratio of the numbers?

1 Answer
Feb 15, 2016

3:4

Explanation:

Call the numbers x and y.

We are given:

x+y=14

x^2+y^2=100

From the first equation, y = 14-x, which we can substitute in the second to get:

100 = x^2+(14-x)^2= 2x^2-28x+196

Subtract 100 from both ends to get:

2x^2-28x+96 = 0

Divide through by 2 to get:

x^2-14x+48 = 0

Find a pair of factors of 48 whose sum is 14. The pair 6, 8 works and we find:

x^2-14x+48 = (x-6)(x-8)

So x=6 or x=8

Hence (x, y) = (6, 8) or (8, 6)

The ratio of the two numbers is therefore 6:8, i.e. 3:4