2 consecutive perfect squares differ by 999. What is the larger of these squares?
The larger perfect square = 500^2 =250,000
The smaller perfect square =499^2 =249,001
250,000 - 249,001 =999 - difference
+2862 x2 is the first number
(x + 1)2 is the second number
These numbers are consecutive.
(x+1)2 - x2 = 999 (they differ by 999)
Expand (x+1)2 , 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.
