If x + 1/x = 5/2, then possible value of x^5 + 1/x^2 is

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26 May 2022 Algebra

If x + 1/x = 5/2, then possible value of x^5 + 1/x^2 is

OPtion

1) 16.03125
2) 4.0625
3) 32.125
4) 4.125
5) 32.25
6) 8.03125
7) 4.25
8) 16.125
9) 8.125
10) None of these

Solution

x + 1/x = 5/2
2x² - 5x + 2 = 0
(x-2) (2x-1) = 0
⇒ x=2 or 1/2
For x=2, x^5 + 1/x^2 = 2^5 + 1/2^2 = 32 + 0.25 = 32.25
For x=1/2, (1/2)^5 + 1/(1/2)^2 = 0.03125 + 4 = 4.03125
So, from the given options 32.25 is correct

Correct Option: 5 Best Solution (1)