Question

The difference between squares of two numbers is 120. The square of small
number is twice the greater number. Find the numbers​

Answer 1

Answer:

          The smaller is 2√6 and the larger is 12.

Step-by-step explanation:

Let y be the smaller number and x the larger number.

    The square of small number is twice the greater number

⇒  y² = 2x.

    The difference between squares of two numbers is 120

⇒  x² - y² = 120

⇒  x² - 2x = 120

⇒  x² - 2x + 1 = 121

⇒  (x - 1)² = 11²

⇒  x - 1 = ±11

⇒  x = -10 or 12

But x = y²/2 is positive, so x = 12 and y = √(2x) = √24 = 2√6.