Number System

Quantitative Aptitude (CPO)

Title

45:30

8 of 24 completed

5 of 15 completed

38 of 100 completed

8 of 20 completed

Indian Economy - Understanding the basics of Indian economic system

If N = (√6 - √5)/(√6 + √5), then what is the value of N + (1/N)?

Let’s break this down step by step:

- Take N = (v6 - v5)/(v6 + v5)

- To find N + (1/N), we’ll calculate 1/N first.

Flip N:

- 1/N = (v6 + v5)/(v6 - v5)

Now, add N and 1/N:

- N + 1/N = (v6 - v5)/(v6 + v5) + (v6 + v5)/(v6 - v5)

Let’s get common denominators and add up:

- N + 1/N = [ (v6 - v5)² + (v6 + v5)² ] / [ (v6 + v5)(v6 - v5) ]

Numerator:

- (v6 - v5)² = 6 - 2v30 + 5 = 11 - 2v30

- (v6 + v5)² = 6 + 2v30 + 5 = 11 + 2v30

- Add: (11 - 2v30) + (11 + 2v30) = 22

Denominator:

- (v6 + v5)(v6 - v5) = 6 - 5 = 1

So,

- N + 1/N = 22 / 1 = 22

Option:4, 22 is correct.

The other options (1, 10, 11, 12) are way off because they don't add up given the arithmetic above. No way around it—the answer's 22.