Reciprocal Equations | MCQs

Explanation

Calculation:

Let, the present age of A = A

2 years ago, his age = A - 2

2 years from now, his age = A + 2

According to the question,

⇒  =  1/A - 2 + 1/A + 2 = 2/3

⇒ 3(A + 2 + A - 2) = 2(A + 2)(A - 2)

⇒ 6A = 2(A2 - 22)

⇒ A2 - 3A - 4 = 0

⇒ A2 + A - 4A - 4 = 0

⇒ A(A + 1) - 4(A + 1) = 0

⇒ (A - 4)(A + 1) = 0

⇒ A = 4 or -1

Since, age can't be negative A = 4

∴ The present age of A is 4 years.

Explanation

Given x + 1/x = 5

To find x² + 1/x²:

(x + 1/x)² = x² + 2(x)(1/x) + 1/x²

= x² + 2 + 1/x²

x² + 1/x² = (x + 1/x)² - 2

= 5² - 2

= 25 - 2

= 23

Explanation

Let's denote the number as x.

Given:

(1/3)x = 3(1/x)

Multiplying both sides by 3x:

x^2 = 9

Solving for x:

x = ±√9

x = ±3