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.

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) (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) (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.

RELATED QUESTIONS
Two positive numbers, which have a difference of 3, are squared. The difference in the... (answered by ikleyn)
The difference of two positive numbers is 3 and their difference of their squares is 69.... (answered by Edwin McCravy)
One positive number is 10 times another number. The difference between the two numbers is (answered by Stitch)
find the two numbers, two positive two-digit numbers have a difference of 6 and multiply... (answered by MathTherapy)
Two positive numbers have a product of 120 and a difference of 7. What are the two... (answered by Alan3354)
sum of two positive numbers is 126 and the difference is 12. find the two numbers (answered by suruman)
One positive number is one-fifth of another number. The difference between the two... (answered by Cromlix)
One positive number is one-fifth of another number. The difference between the two... (answered by fractalier)
One positive number is 9 times another number. The difference of the two numbers is 744, (answered by josgarithmetic)