# The difference of squares of two numbers is 180.

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.

Solution:

Let the larger numbers be $x$

Then according to question,

Square of the smaller number be $=8 x$ then

$x^{2}-8 x=180$

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

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

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

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

$(x-18)=0$

$x=18$

Or

$(x+10)=0$

$x=-10$

Since, being a positive integer so, x cannot be negative,

Therefore,

When $x=18$ then smaller number be

$\sqrt{8 x}=\sqrt{8 \times 18}$

$=\sqrt{144}$

$=\pm 12$

Thus, two consecutive number be 18,12 or $18,-12$