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Question
If `x + 1/x = 5`, find the value of `x^4 + 1/x^4`.
Sum
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Solution
Given: `x + 1/x = 5`
Step-wise calculation:
1. Square both sides to find `x^2 + 1/x^2`:
`(x + 1/x)^2 = 5^2`
`x^2 + 2 + 1/x^2 = 25`
`x^2 + 1/x^2 = 25 - 2`
`x^2 + 1/x^2 = 23`
2. Square again to find `x^4 + 1/x^4`:
`(x^2 + 1/x^2)^2 = 23^2`
`x^4 + 2 + 1/x^4 = 529`
`x^4 + 1/x^4 = 529 - 2`
`x^4 + 1/x^4 = 527`
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Chapter 3: Expansions - Exercise 3B [Page 72]
