Question

x - 1/x = 4,
then find the value of :
x⁴ + (1/x⁴)


source : advisor textbook (class 8)​

Answer 1

Answer :-

x⁴ + 1/x⁴ = 322

$\rule{150}2$

Given:-

• $\sf{x\:-\:\dfrac{1}{x}\:=\:4}$

Find:-

$\sf{x^4\:+\:\dfrac{1}{x^4}}$

Solution:-

$\implies\:\sf{\bigg(x\:-\:\dfrac{1}{x}\bigg)^2\:=\:(4)^2}$

(a + b)² = a² + b² + 2ab

$\implies\:\sf{x^2\:+\:\dfrac{1}{x^2}\:-\:2x\dfrac{1}{x}\:=\:16}$

$\implies\:\sf{x^2\:+\:\dfrac{1}{x^2}\:-\:2\:=\:16}$

$\implies\:\sf{x^2\:+\:\dfrac{1}{x^2}\:=\:16\:+\:2}$

$\implies\:\sf{x^2\:+\:\dfrac{1}{x^2}\:=\:18}$

Now, do squaring on both sides

(a²)² + (b²)² = a⁴ + b⁴ + 2a²b²

$\implies\:\sf{\bigg(x^2\:+\:\dfrac{1}{x^2}\bigg)^2\:=\:(18)^2}$

$\implies\:\sf{x^4\:+\:\dfrac{1}{x^4}\:+\:2x^2\dfrac{1}{x^2}\:=\:324}$

$\implies\:\sf{x^4\:+\:\dfrac{1}{x^4}\:+\:2\:=\:324}$

$\implies\:\sf{x^4\:+\:\dfrac{1}{x^4}\:=\:324\:-\:2}$

$\implies\:\sf{x^4\:+\:\dfrac{1}{x^4}\:=\:322}$

Answer 2

Answer:

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