Question

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

Answer 1

Let the numbers be x and y,

also x>y.

A.T.Q,

x² - y² = 180 -------(i)

y² = 8x --------(ii)

x² - 8x = 180

x² - 8x - 180 = 0

x² - 2 • x • 4 + 4² - 180 = 4²

(x - 4)² = 16 + 180

(x - 4)² = 196

x - 4 = ± 14

Case 1, x - 4 = 14

x - 4 = 14

x = 18

Case 2, x - 4 = -14

x - 4 = -14

x = -10

Now,

x² - y² = 180

18² - y² = 180

-y² = -144

y² = 144

y = 12,

Therefore, [x = 18] and [y = 12]