Problema Solution

The difference of two positive numbers is 5 and the sum of their squares is 37. Find the numbers.

The bigger number is ____, and the smaller number is _____.

Answer provided by our tutors

Solution:

x = 1st number

y = 2nd number

 

x - y = 5

y = x - 5

 

x^2 + y^2 = 37

x^2 + (x-5)^2 = 37

x^2 + x^2 - 10x + 25 = 37

2x^2 - 10x - 12 = 0

x^2 - 5x - 6 = 0

(x-6)(x+1) = 0

x = 6

x = -1 ==> invalid

 

y = 6 - 5

y = 1

 

bigger = 6

smaller = 1