Question

The differences of squares of two numbers is 180. the square of the smaller number is 8 times the larger number. find the 2 numbers.

Answer 1

I think 12 is your answer

Answer 2

let the two number be x and y

according to first condition,

x^2 - y^2 = 180 - 1

according to the second conditions,

x^2 = 8y^2

x^2 - 8y^2 =0 - 2

subtracting equation 1 by 2

x^2 - y^2 = 180
-x^2-8y^2 = 0
------------------------
9y^2 = 180
y^2 =180/9 = 20

$y = \sqrt{20 } = \: 4 \sqrt{5}$
placing the value of y in equation 1

x^2 - 80 = 180
x^2 = 180 - 80= 100
x = 10

numbers are

$4 \sqrt{5} \: and \: 10$