Question

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Answer 1

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

Given that Difference between squares of two numbers is 120.

= > y^2 - x^2= 120. ---- (1)

Given that Square of smaller number is twice the greater number.

= > x^2 = 2y ----- (2)

Substitute (2) in (1), we get

= > y^2 - 2y = 120

= > y^2 - 2y - 120 = 0

= > y^2 - 12y + 10y - 120 = 0

= > y(y - 12) + 10(y - 12) = 0

= > (y - 12)(y + 10) = 0

= > y = 12, y = -10[Since y cannot be negative]

Substitute y = 12 in (1), we get

= > x^2 = 2y

= >x^2 = 2(12)

= > x^2 = 24

$= > x = \sqrt{24}$

$= > x = 2\sqrt{6}$

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Therefore, the numbers are:

$= > \boxed{y = 12, x = 2\sqrt{6}}}$

Hope this helps!