Question

x+1/x =2,find the value of x^9+1/x^9
step wise step solution best answer I will mark as brainlist ​

Answer 1

$\bigstar$ Answer :

$\bold{x+\frac{1}{x}=2 }\\\\\bold{Cubing\;on\;sides\;,we\;get\;,}\\\\\bold{(x+\frac{1}{x})^3=8}\\\\\bold{x^3+\frac{1}{x^3}+3.x.\frac{1}{x}(x+\frac{1}{x} )=8 }\\\\\bold{x^3+\frac{1}{x^3} +3(2)=8}\\\\\bold{x^3+\frac{1}{x^3}=2}\\\\\bold{Once\;again\;cubing\;on\;both\;sides\;,we\;get\;,}\\\\\bold{(x^3+\frac{1}{x^3})^3=8}\\\\\bold{x^9+\frac{1}{x^9}+3.x^3.\frac{1}{x^3}(x^3+\frac{1}{x^3})=8}\\\\\bold{x^9+\frac{1}{x^9}+3(2)=8}\\\\\bold{x^9+\frac{1}{x^9}=8-6}\\\\\bold{x^9+\frac{1}{x^9}=2}$