 Hello and welcome to the session. Let us understand the following problem today. The difference of squares of two numbers is 180. The square of the smaller number is a times the larger number, find the two numbers. Now let us write the solution. Let the larger number be x. The square of the smaller number is equal to 8x and square of larger number is equal to x square. Difference of two squares is equal to 180. Therefore the equation form will be x square minus 8x is equal to 180. Now solving this we get x square minus 8x minus 180 is equal to 0. Now splitting the middle term we get x square minus 18x plus 10x minus 180 is equal to 0 which implies x taking common x minus 18 plus 10 taking common x minus 18 which is equal to 0. Therefore this implies x plus 10 into x minus 18 is equal to 0 which implies x is equal to minus 10 and x is equal to 18. Now case one, when x is equal to 18 the square of smaller number is equal to 18 into 8 which is equal to 144. Therefore smaller number is equal to plus minus 12. Thus the numbers are 12 or 18 comma minus 12. Now case two, when x is equal to minus 10. Now we have smaller number is equal to 8x which is equal to 8 into minus 10 which is equal to minus 18. But the square of number is always positive. Therefore x is equal to minus 10 is not possible. Therefore the required numbers comma 12, 18 comma minus 12. I hope you understood the problem. Bye and have a nice day.