Question

The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

Answer 1

Let the smaller numbers be x

Then according to question,

The larger number be = 2x - 5, then

(2x - 5)² - x² = 88

4x² - 20x + 25 - x² - 88 = 0

3x² - 20x - 63 = 0

3x² - 27x + 7x - 63 = 0

3x(x - 9) + 7(x - 9) = 0

(x - 9)(3x + 7) = 0

x - 9 = 0

x = 9

Or

3x + 7 = 0

3x = -7

x = `-7/3`

Since, x being a positive integer so, x cannot be negative,

Therefore,

When x = 9 then larger number be

2x - 5 = 2(9) - 5 = 18 - 5 = 13

Thus, two consecutive number be either 9, 13.