Question

The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.

Answer 1

Let the numbers be integers. One of the numbers be x. So, the other will be (2x - 3).

Then according to question,

x² + (2x - 3)² = 233

x² + 4x² - 12x + 9 = 233

5x² - 12x + 9 - 233 = 0

5x² - 12x - 224 = 0

5x² - 40x + 28x - 224 = 0

5x(x - 8) + 28(x - 8) = 0

(x - 8)(5x + 28) = 0

x - 8 = 0

x = 8

Or

5x + 28 = 0

5x = -28

x = -28/5

Since, we have assumed the numbers to be integers, so x cannot be a rational number/fraction.

Therefore, for x = 8

Other number = (2x - 3) = 2(8) - 3 = 16 - 3 = 13

Thus, whole numbers be 8, 13.