Given that w>0w>0 and that w1w=7w1w=7, find the value of (w+1w)2(w+1w)2.


Answer:

5353

Step by Step Explanation:
  1. We are given, w>0w>0 and w1w=5w1w=5 and we need to find the value of (w+1w)2(w+1w)2.
  2. (w+1w)2=w2+1w2+2(w)(1w)(w+1w)2=w2+1w2+2
    Adding and subtracting 2 on RHS, we get,
    (w+1w)2=w2+1w2+2+22(w+1w)2=w2+1w22(w)(1w)+4(w+1w)2=(w1w)2+4(w+1w)2=72+4(w+1w)2=53
  3. Hence, the value of (w+1w)2 is 53.

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