SOLUTION: Write a quadratic equation and solve The difference of two numbers is 6 and the difference of their squares is 60. Find the numbers

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Question 1027956: Write a quadratic equation and solve
The difference of two numbers is 6 and the difference of their squares is 60. Find the numbers
Found 2 solutions by mananth, Theo:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let one number be x
other will be x+6
(x+6)^2-x^2 = 60
x^2+12x+36 -x^2=60
12x+36-60
12x =24
x=2
2& 8 are the numbers

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.

you get:

a - b = 6
a^2 - b^2 = 60

in the first equation, solve for a to get a = b + 6

in the second equation, replace a with (b+6) to get:

(b+6)^2 - b^2 = 60

simplify to get:

b^2 + 12b + 36 - b^2 = 60

combine like terms to get:

12b + 36 = 60

subtract 36 from both sides of this equation to get:

12b = 24

solve for b to get:

b = 2

if b = 2, the a - b = 6 becomes a - 2 = 6

add 2 to both sides of this equation to get a = 8

when a = 8 and b = 2, you get:

a - b = 8 - 2 = 6
a^2 - b^2 = 8^2 - 2^2 = 64 - 4 = 60

this confirms the solution is correct.

the numbers are 8 and 2.

subtract the smaller number from the larger number and you get 6.

subtract the square of the smaller number from the square of the larger number and you get 60.