Question

if X+1/x =6 then the value of x4+1/x4 is ​

Answer 1

Solution:

It is given that,.

x+1/x = 6 ----(1)

x²+1/x² = (x+1/x)²-2

= 6² - 2

= 36 - 2

= 34 ------(2)

x⁴+1/x⁴ = (x²+1/x²)² - 2

= 34² - 2

= 1156- 2

= 1154

Therefore,.

x⁴ + 1/x⁴ = 1154

••••

Answer 2

Given :

$x+\dfrac{1}{x}=6$

To find :

$x^4+\dfrac{1}{x^4}=?$

Solution :

Squaring the given equation :

$x^2+\dfrac{1}{x^2}+2=6^2\\\\x^2+\dfrac{1}{x^2}=36-2\\\\x^2+\dfrac{1}{x^2}=34$

Again squaring the last step :

$x^4+\dfrac{1}{x^4}+2=34^2\\\\x^4+\dfrac{1}{x^4}=1156-2\\\\x^4+\dfrac{1}{x^4}=1154$

Hence, the required value is 1154.