Question

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

Answer 1

Let larger number = x

Smaller number = y

According to first condition of question

x² – y² = 180 …(i)

According to second condition of question

y² = 8x …(ii)

Putting value of y² from equation (ii) in equation (i)

x² – 8x = 180

⇒ x² – 8x – 180 = 0

Comparing it by ax² + bx + c = 0

a = 1, b = -8, c = -180

Then by  quadratic formula

Thus x = 18 and -10

When x = 18, then from equation (ii)

y² = 8 × 18 = 144

⇒ y = ±√144

⇒ y = ± 12

When x = -10, then from equation (ii)

y² = 8 × (-10)

⇒ y² = -80 (not possible)

∴ y = ± 12

y = + 12 and – 12

Hence, required numbers will be 18 and 12 or 18, -12