If N radic 6 radic 5 radic 6 radic 5 then what is the value of N 1 N ........

Quantitative Aptitude (CPO) Algebra

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

Let’s break this down step by step:

- Start with N = (v6 - v5) / (v6 + v5).

- First, find 1/N. Flip and rationalize: 1/N = (v6 + v5)/(v6 - v5)

- Multiply top and bottom by the conjugate (v6 + v5) to rationalize:

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

- That gives (v6 + v5)^2 / [(v6)^2 - (v5)^2] = (6 + 2v30 + 5) / (6 - 5)

- So numerator: 11 + 2v30, denominator: 1 --> 1/N = 11 + 2v30

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

- Combine over common denominator: [(v6 - v5)^2 + (v6 + v5)^2] / [(v6 + v5)(v6 - v5)]

- Work out numerator: (6 - 2v30 + 5) + (6 + 2v30 + 5) = (11 - 2v30) + (11 + 2v30) = 22

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

So N + 1/N = 22

Option:4, 22

Here’s what matters:

- Option 1 (10), 2 (11), 3 (12) – These come from not following through on the radical simplification or making algebra mistakes along the way.

- Option 4 (22) – It’s correct when you do the full expansion and cancellation.

In short, the correct and final answer is Option 4, 22. This isn’t obvious at first glance, but the algebra is solid.

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