Question

The difference between squares of two numbers
is 12o. The square of smaller number is twice the greater number. find the number​

Answer 1

Answer:

Greater number is 12

And smaller number is 2√6

Answer 2

Answer:

smaller and greater number is

$2\sqrt{6} \: and \: 12 \: respectively$

Explanation:

Let smaller and greater number be x and y respectively

from first condition

${y}^{2} - {x}^{2} = 120 ...........(1)$

from second condition

${x}^{2} = 2y..................(2)$

from second equation

${ y}^{2} - 2y - 120 = 0$

${y}^{2} - 12y + 10y - 120 = 0 \\ y(y - 12) + 10(y - 12) = 0$

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

y-12=0 and y+10=0

y=12 and. y=-10

according to second equation

y=-10 is unacceptable

${x}^{2} = 2y \\ {x}^{2} = 2 \times 12 \\ {x}^{2} = 24 \\ x = 2\sqrt{6}$