Question

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

Answer 1

Let the larger number be x and smaller number be y

$x^2-y^2$ = 180 ... (1)

Also given the square of smaller number is 8 times the larger number

$y^2=8x$

substitute this value in equation (1) we get

$x^2-8x=180$

$x^2-8x-180=0$

$x^2-18x+10x-180=0$

$x(x-18)+10(x-18)=0$

$(x-18)(x+10)=0$

x=18, x= -10

Since x cannot be negative

x= 18 then

$y^2=8x=8\left(18\right)=144$

y=12