Question

The difference of two positive numbers is 5 and the sum of their squares is 233. What are the numbers?

Answer 1

Answer:

13 and 8

Step-by-step explanation:

a-b = 5

==> a = b+5

a^2 + b^2 = 233

plug in a = b+5: (b+5)^2 + b^2 = 233

b^ + 10b + 25 + b^2 = 233

2b^2 + 10b -208 = 0

use the quadratic formula:

b = 8 or -13 (-13 doesn't work cuz it asks for positive numbers)

so if b = 8, then a = 5+b = 5+8 = 13