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 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
