Question

The difference of square of two natural numbers is 84. The square of the large number is 25 time smaller number. Find the number.

Using one variable only

Answer 1

Let the smaller number be x

Larger number be y

The square of larger number, y^2 = 25x

According to the question,

y^2- x^2 = 84

25x - x^2 = 84

x^2 - 25x + 84 =0

x^2 - 21x- 4x +84 = 0

x (x-21) - 4 (x-21) = 0

(x-21) (x-4) = 0

The value of x is 21 or 4

Smaller number = 21 or 4

Larger number = 25×21 = 525

= 25 × 4 = 100

Hope it will help you