If x-\frac{1}{x}=3, then the value of x^4+\frac{1}{x^4} is

Sainik School Entrance Exam 2021 Solved Paper

Question : 21 of 150

Marks: +1, -0

x-{1}/{x}=3

, then the value of

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

Solution:

(b)

x-{1}/{x}=3, x^4+{1}/{x^4}=

x-{1}/{x}=3

Squaring on both sides,

(x-{1}/{x})^2=3^2

⇒ x^2+{1}/{x^2}-2(x.{1}/{x})=9

⇒ x^2+{1}/{x^2}=11

Again squaring on both sides

(x^2+{1}/{x^2})^2=11^2

⇒ x^4+{1}/{x^4}+2(x^2.{1}/{x^2})=121

∴

x^4+{1}/{x^4}=119 .

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