Question

Plz solve this ....
X+1/X=6
X⁴+1/X⁴=?
​

Answer 1

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

squaring on both sides

(x+ 1/x)^2 = 6^2

x^2 + 1/x^2 + 2*x* 1/x = 36

x^2 + 1/x^2 + 2= 36

x^2 + 1/ x^2 = 34.......(2)

now , squaring on both sides in (2)

(x^2 + 1/x^2)^2= 34^2

x^4 + 1/x^4 + 2*x^2 * 1/x^2 = 1156

x^4 + 1/ x^4 = 1156-2= 1154

Answer 2

First of all we will write down the original equation as it exists in the question

x+ 1/x = 6

Now, on squaring on both sides of this equation, we get :

(x+ 1/x)² = 6²

Or, x² + 1/x² + 2.x.1/x = 36

Or, x² + 1/x² + 2 = 36

Or, x² + 1/ x² = 34.......(i)

Again, squaring on both sides of the equation (i)

(x² + 1/x²)²= 34²

Or, x⁴ + 1/x^⁴ + 2.x².1/x² = 1156

Or, x⁴ + 1/ x⁴ = 1156 - 2= 1154

Or, x⁴ + 1/ x⁴ = 1154 [ANS.]