If x^{8}-2599 x^{4}+1=0, then the positive value of x-\frac{1}{x} will be

SSC CHSL 19 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 52 of 100

Marks: +1, -0

x^{8}-2599 x^{4}+1=0

, then the positive value of

x-\;{1}/{x}

will be

Solution:

Given,

⇒\;x^{8}-2599 x^{4}+1 \;\; =0

⇒\;x^{8}+1 \;\; =2599 x^{4}

⇒\;x^{4}+\;{1}/{x^{4}} \;\; =2599

We know,

(x^{2}+\;{1}/{x^{2}})^{2}=x^{4}+\;{1}/{x^{4}}+2

So,

(x^{2}+\;{1}/{x^{2}})^{2}=2599+2=2601

⇒ \;\; x^{2}+\;{1}/{x^{2}} \;\; =√{2601}=51

∵ \;\; (x-\;{1}/{x})^{2} \;\; =x^{2}+\;{1}/{x^{2}}-2

\;\; =51-2=49

∴

The positive value of

x-\;{1}/{x}=√{49}=7

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