SOLUTION: Two positive numbers, which have a difference of 3, are squared. The difference in the results is 81. Find the two numbers with working.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Two positive numbers, which have a difference of 3, are squared. The difference in the results is 81. Find the two numbers with working.      Log On


   

Question 1095691: Two positive numbers, which have a difference of 3, are squared. The difference in the results is 81. Find the two numbers with working.
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Two positive numbers, which have a difference of 3, are squared. The difference in the results is 81. Find the two numbers with working.
(x+3)^2 - x^2 = 81
6x + 9 = 81
x = 12
--> 12 & 15

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let a be the larger number
let b be the smaller number

a - b = 3

a^2 - b^2 = 81

since a^2 - b^2 is equal to (a - b) * (a + b), then:

(a - b) * (a + b) = 81

since a - b = 3, then:

3 * (a + b) = 81

since a - b = 3, then a = b + 3 then:

3 * (a + b) = 81 becomes 3 * (b + 3 + b) = 81

simplify to get 3 * (2b + 3) = 81

simplify further to get 6b + 9 = 81

solve for b to get b = (81 - 9) / 6 = 12

since a = b + 3, then a = 15

your larger number is 15 and your smaller number is 12.

15 - 12 = 3

15^2 - 12^2 = 225 - 144 = 81

your solution is that the two number are 15 and 12.