Question

The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.Solve the word problem

Answer 1

$given \: \: {x}^{2} - {y}^{2} = 120 \: \: and \\ {y}^{2} = 2x \\ therefore \: {x}^{2} - 2x - 120 = 0 \\ (x - 12)(x + 10) = 0 \\ x = 12 \: \: or \: \: x = - 10 \\ x = - 10 is \: not \: possible \\ therefore \: numbers \: are \\ 12 \: \: and \: \: \sqrt{24} = 2 \sqrt{6}$