SOLUTION: please help me solve this equation The difference between the squares of two odd numbers is 48. What are the numbers? i have been given a tip which is if the larger of the two num

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Question 392639: please help me solve this equation
The difference between the squares of two odd numbers is 48. What are the numbers? i have been given a tip which is if the larger of the two numbers is x, then the smaller number is x-2. Form an equation and solve?
Please would you help me solve and show me how to work it out please?
Found 3 solutions by richard1234, mananth, stanbon:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Just use

x%5E2+-+%28x-2%29%5E2+=+48

4x+-+4+=+48 (x^2 cancels out)

x = 13, so 13 and 11 are the numbers. Note that -11, -13 also satisfies since we can use

%28x-2%29%5E2+-+x%5E2+=+48 and get a linear equation.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between the squares of two odd numbers is 48. What are the numbers? i have been given a tip which is if the larger of the two numbers is x, then the smaller number is x-2. Form an equation and solve?
Please would you help me solve and show me how to work it out please?
...
let the odd numbers be n & n+2
...
(n+2)^2-n^2=48
n^2+4n+4-n^2=48
4n+4=48
4n=48-4
4n=44
/4
n=11
..
11 & 13 are the numbers
..
m.ananth@hotmail.ca

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between the squares of two odd numbers is 48.
1st odd: 2x-1
2nd odd: 2x+1
-------
What are the numbers?
---
Form an equation and solve?
(2x-1)^2 - (2x+1)^2 = 48
4x^2-4x+1-[4x^2+4x+1] = 48
----
-8x = 48
x = -6
---
1st: 2x-1 = -13
2nd 2x+1 = -11
----
Check:
(-13)^2-(-11)^2 = 48
169 - 121 = 48
48 = 48
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Note: You could also use the equation (2x+1)^2-(2x-1)^2 = 48
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By the way, x and x-2 do not represent 2 odd numbers. Odd
numbers are always one less than or one greater than an
even number.
Use 2x-1 and 2x+1 to represent 2 consecutive odd numbers.
==================
Cheers,
Stan H.