Question
Download Solution PDFComprehension
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 V + W equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
(8 + 3√7) 20 = U + V...(i)
(8 - 3√7) 20 = W...(ii)
Here, 0 < W < 1
Now, adding Eqs. (i) and (ii), we get
U + V +W = (8 + 3√7) 20 + (8 - 3√7) 20
= 2[20C0820+ 20C2818. (3√7 )2+........+(3√7)20
⇒ It is an even number.
Also, 0 < V < 1, 0 < W < 1 and U is an integer
Thus, V + W is an integer
V + W = 1
∴ Option (d) is correct.
Last updated on May 30, 2025
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