SOLUTION: The difference of squares of two consecutive even natural numbers is 60. Find the numbers.

Question 1019942: The difference of squares of two consecutive even natural numbers is 60. Find the numbers.
Found 3 solutions by stanbon, ikleyn, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The difference of squares of two consecutive even natural numbers is 60. Find the numbers.
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1st:: 2x
2nd: 2(x+1)
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[2(x+1)]^2 - (2x)^2 = 60
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4[x^2 + 2x + 1] - 2x^2 = 60
2x^2 + 4x + 4 = 60
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x^2 + 2x - 56 = 0
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x = 6.55
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Note:: That would mean that 2x is NOT a natural number.
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Ans:: None
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Cheers,
Stan H.
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Answer by ikleyn(52848)   (Show Source): You can put this solution on YOUR website!
.
The difference of squares of two consecutive even natural numbers is 60. Find the numbers.
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1st:: 2x
2nd: 2(x+1)
-------
[2(x+1)]^2 - (2x)^2 = 60
-------
4[x^2 + 2x + 1] - 4x^2 = 60
4x^2 + 8x + 4 - 4x^2 = 60
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8x - 56 = 0
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x = 7

First number = 2x = 14
Second nimber = 2x + 2 = 16
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Check: 16^2 - 14^2 = 256 - 196 = 60.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

The difference of squares of two consecutive even natural numbers is 60. Find the numbers.

Let smaller number be S
Then larger number = S + 2
We then get:

4S + 4 = 60
4S = 56
S, or smaller number = , or
Larger number: 14 + 2, or
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