The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Let the larger and smaller number be x and y respectively.
According to the given question,
= x2 – y2 = 180 and y2 = 8x
= x2 – 8x = 180
= x2 – 8x – 180 = 0
= x2 – 18x +10x – 180 = 0
= x(x – 18 ) +10(x – 18 ) = 0
= (x – 18 )(x+10) = 0
= x = 18, -10
The larger number cannot be negative as it makes square of smaller number negative, which is not possible.
Therefore, the larger number will be 18 only.
X = 18
∴ y2 = 8x = 8×18 = 144
= 
∴ smaller number = 
Therefore, the numbers are 18 and 12 or 18 and −12.
10