Comprehension

Direction : Consider the following for the items that follow :  

Let (8 + 3√7) 20  = U + V and (8 - 3√7) 20  = W, where U is an integer and 0 < V < 1.

What is the value of (U + V)W? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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Answer (Detailed Solution Below)

Option 2 : 1
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Detailed Solution

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Explanation:

Given:

(8 + 3√7) 20  = U + V...(i)

(8 - 3√7) 20  = W...(ii)

⇒ (U + V)W =] (8 + 3√7) 20][(8 - 3√7) 20]

= (64 – 63)20 = 120 = 1

∴ Option (b) is correct.

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