<PRE><B>Question 1142283</B>
 One positive number exceeds another positive number by 5 . 
 The sum of their squares is 193.
 find the numbers
:
x^2 + (x+5)^2 = 193
FOIL (x+5)(x+5)
x^2 + x^2 + 10x + 25 = 193
2x^2 + 10x + 25 - 193 = 0
2x^2 + 10x - 168 = 0
simplify, divide by 2
x^2 + 5x - 84 = 0
easily factors to
(x+12)(x-7) = 0
the positive solution
x = 7
:
:
Check: 7^2 + 12^2  =
49 + 144 = 193
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