Pre algebra word problem

Question

Find 2 consecutive positive odd numbers such that if the square of the smaller is subtracted from the larger the result is 56

Answer 1

The answer to this question is 13,15, which are the two consecutive positive odd integers that answer this question. We can obtain this answer using the following method:

Start by assigning the variable x to the larger number, which leaves the expression x-2 to represent the smaller number (as odd numbers are 2 apart)

x² - (x-2)² = 56

x² - (x² -4x + 4) = 56 >Expanded using polynomial multiplication (x-2)*(x-2)

x² - x^{2 +}4x - 4 = 56

4x - 4 = 56

4x - 4 + 4 = 56 + 4 > Using the additive property of equality

4x = 60

4x/4 = 60/4 > Using the division property of equality

x = 15

Therefore, we get a value of 15 for x, or the larger number, so x-2=13, the smaller number, giving us an answer of 13 and 15 as the two consecutive positive odd integers that have a difference of 56 between their squares.