the difference between the squares of two consecutive odd numbers is 128. What is the product of the two integers?
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Let the 2 consecutive odd numbers are (n-1) and (n+1).
(n+1)^2 - (n-1)^2 = 128
Expanding and simplifying the terms,
4n = 128
n = 32
The 2 odd numbers are 31 and 33.
(n+1)^2 - (n-1)^2 = 128
Expanding and simplifying the terms,
4n = 128
n = 32
The 2 odd numbers are 31 and 33.
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(2x + 3)^2 - (2x + 1)^2 = 128
(2x + 3) * (2x + 1) = ?
(2x + 3)^2 - (2x + 1)^2 = 128
4x^2 + 12x + 9 - 4x^2 - 4x - 1 = 128
8x + 8 = 128
x + 1 = 16
x = 15
2x + 3 = 33
2x + 1 = 31
33 * 31 = (32 + 1) * (32 - 1) = 32^2 - 1^2 = 1024 - 1 = 1023
1023
(2x + 3) * (2x + 1) = ?
(2x + 3)^2 - (2x + 1)^2 = 128
4x^2 + 12x + 9 - 4x^2 - 4x - 1 = 128
8x + 8 = 128
x + 1 = 16
x = 15
2x + 3 = 33
2x + 1 = 31
33 * 31 = (32 + 1) * (32 - 1) = 32^2 - 1^2 = 1024 - 1 = 1023
1023