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x^4 + 1/x^4 given, x > 0: find an odd power x^5 or x^7 + 1/x^n

This type of question, asked 2 times: 14 Jul 2023 S4, 20 Jul 2023 S2. All 2 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S4

    69
    If x>0x > 0, and x4+1x4=254x^4 + \frac{1}{x^4} = 254, what is the value of x5+1x5x^5 + \frac{1}{x^5}?

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  2. Question 2

    20 Jul 2023 S2

    53
    If x>0x > 0 and x4+1x4=142x^4 + \frac{1}{x^4} = 142, what is the value of x7+1x7x^7 + \frac{1}{x^7}?

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