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 _____.
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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