Simple

Algebra Level 3

x = 1 + 2016 2 x=\dfrac{1+{\sqrt{2016}}}{2}

Evaluate 4 x 2017 − 4 x 2016 − 2015 x 2015 4x^{2017} - 4x^{2016} - 2015x^{2015} .


The answer is 0.

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Budi Utomo by Budi Utomo , 23, Indonesia

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2 solutions

Rishabh Jain
Jan 21, 2016

x= 1 + 2016 2 \dfrac{1+{\sqrt{2016}}}{2} ⇒ 2 x − 1 = 2016 \Rightarrow 2x-1=\sqrt{2016} Squaring both sides we get, 4 x 2 − 4 x − 2015 = 0 4x^2-4x-2015=0 Multiplying the equation by x 2015 x^{2015} , we get what is required i.e 4 x 2017 − 4 x 2016 − 2015 x 2015 = 0 \color{forestgreen}{4x^{2017} - 4x^{2016} - 2015x^{2015}=0}

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I only got this since the related quiz was about quadratics. Other than this, what would indicate that converting x = bleh into quadratic form would resemble 4x^2017 - bleh?

Bryan Hung - 5 years, 4 months ago

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One cannot go calculating x 2017 , x 2016 , x 2015 x^{2017}, x^{2016},x^{2015} ... Some more manipulations might have been needed but this question's demand was to write the given information in desired form and square to get what is required..

Rishabh Jain - 5 years, 4 months ago
Kamalpreet Singh
Jan 25, 2016

It was quite easy for me to find out its answer which is 0

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