What is V+W equal to?
Direction: Consider the following for the two (02) items that follow :<br>Let (8+3\sqrt{7})^{20}=U+V and (8-3\sqrt{7})^{20}=W, where U is an integer and 0 \lt V \lt 1.
- A. 8
- B. 4
- C. 2
- D. 1 ✓
Correct Answer: D. 1
Explanation
Since 0 \lt 8-3\sqrt{7} \lt 1, it follows that 0 \lt W \lt 1. The sum (8+3\sqrt{7})^{20} + (8-3\sqrt{7})^{20} = U+V+W yields an even integer I because the irrational terms cancel out. Since U and I are integers, V+W must also be an integer. Given 0 \lt V \lt 1 and 0 \lt W \lt 1, their sum V+W must be strictly between 0 and 2. The only integer in this range is 1.
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