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Algebra Level 3

If x + 1 x = 3 x+\dfrac{1}{x} = 3 , then what is the value of x 16 + 1 x 16 x^{16}+\dfrac{1}{x^{16}} ?


The answer is 4870847.

Sirajum Prince by Sirajum Prince , 27, Bangladesh

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1 solution

Sirajum Prince
Jul 21, 2015

x+1/x=3 =>x^2+1/x^2=7 =>x^4+a/x^4=47 =>x^16+1/x^16=(2207)^2-2

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You're wrong. It should be

x^4 + 1/x^4 = 47 ==> x^8 + 1/x^8 = 2207, x^16 + 1/x^16 = 2207^2 -2

Check the properties of indices again.

Pi Han Goh - 5 years, 10 months ago

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Oh!that was a mistake.sorry!i'll change it.thanks for your correction

Sirajum Prince - 5 years, 10 months ago

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