# 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

#### Explanation:

Call the numbers

We are given:

#x+y=14#

#x^2+y^2=100#

From the first equation,

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

Subtract

#2x^2-28x+96 = 0#

Divide through by

#x^2-14x+48 = 0#

Find a pair of factors of

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

So

Hence

The ratio of the two numbers is therefore