If x^{4}+{1}/{x^{4}}=322, x \neq0, then one of the values of (x-\frac{1}{x}) is

CTET 2 Math and Science Jan 2021 Paper

Question : 51 of 150

Marks: +1, -0

x^{4}+{1}/{x^{4}}=322, x ≠0

, then one of the values of

(x-{1}/{x})

Solution:

x^{4}+{1}/{x^{4}}=322

(We know that

a^{2}+b^{2}=(a+b)^{2}-2 a b)

⇒x^{2}+{1}/{x^{2}}+2=322+2

⇒(x^{2}+{1}/{x^{2}})^{2}=324

⇒x^{2}+{1}/{x^{2}}=18

⇒x^{2}-{1}/{x^{2}}-2=18-2

⇒(x-{1}/{x})^{2}=16

∴x-1/x=4

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