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2 consecutive perfect squares differ by 999. What is the larger of these squares?

 Oct 26, 2019
 #1
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+1

The larger perfect square = 500^2 =250,000

The smaller perfect square =499^2 =249,001

250,000 - 249,001 =999 - difference

 Oct 26, 2019
 #2
avatar+2547 
+2

x2 is the first number

 

(x + 1)2 is the second number

 

These numbers are consecutive.

 

(x+1)2 - x= 999       (they differ by 999)

 

Expand (x+1), then simplify.

 

x2 + 2x + 1 - x2 = 999

 

2x + 1 = 999

 

x = 499

 

Bigger number is 499 + 1 = 500

 

This is how you solve these problems.

CalculatorUser  Oct 26, 2019
edited by CalculatorUser  Oct 26, 2019

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