Question:
If x -1/x = 5, find the values of x2 + 1/x2 and x4 + 1/x4
Answer:
Given, x - 1/x = 5
Now, square on both side, we get
(x + 1/x)2 = 52
=> x2 + 1/x2 + 2 * x * (1/x)= 25
=> x2 + 1/x2 + 2 = 25
=> x2 + 1/x2 = 25 - 2
=> x2 + 1/x2 = 23
Again, square on both side, we get
(x2 + 1/x2 )2 = (23)2
=> x4 + 1/x4 + 2 * x2 * (1/x2 )= 529
=> x4 + 1/x4 + 2 = 529
=> x4 + 1/x4 = 529 - 2
=> x4 + 1/x4 = 527
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