What is the value of (U+V)W?
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. 1/2
- B. 1 ✓
- C. 3/2
- D. 2
Correct Answer: B. 1
Explanation
Substitute the given values into the expression: (U+V)W = (8+3\sqrt{7})^{20}(8-3\sqrt{7})^{20}. Using difference of squares, this is [(8)^2 - (3\sqrt{7})^2]^{20} = (64 - 63)^{20} = 1^{20} = 1.
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