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The positive difference between two consecutive even perfect squares is 228. Compute the larger of the two squares.

 May 24, 2021
 #1
avatar+20 
+1

3364. If we simply this problem to the differnce between 4^2 and 6^2, we see that the differnce is 20. This is basically eaual to the distance between 4^2 and 5^2 plus the distance between 5^2 and 6^2. To calculate the distance I use the formula (sq number, in this example 6 x 2-1), this means the distance from 5^2 to 6^2 is 11, and the distance from 4^2 to 5^2 is 9. We can also takeaway that the differenmce between squares is ALWAYS 2 greater than the last one. 

 

So, back to the problem, we can tell that the squares have to be 113 and 115 apart, which means that 2x-1=115, meaning that x = 58, doing the same thing to 113, means that x = 56. 

 

To check our answers, 58^2 is 3364, and 56^2 is 3136, the difference between these two is 228, meaning that our answer (58^2 or 3364) is correct!

 May 24, 2021
 #2
avatar+34328 
+1

Even squares come from even numbers

 

(x+2)^2  - x^2  = 228

x^2 + 4x + 4   - x^2 = 228

4x = 224

x = 56    x+2 = 58       58^2 = 3364

 May 24, 2021

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