Question

x 1/x =root 3 then what is the value of x^18 +x^12+ x^6 + 1

Answer 1

1/x= √3
(1√3)^18 + (1/√3)^12+(1/√3)^6+1
{1+(√3)^6 + (√3)^12 + (√3)^18}/(√3)^18
{1 + (3)^6/2 + (3)^12/2 + (3)^18/2}/(3)^18/2
{1+3^3+3^6+3^9}/3^9
{1+27+729+19683}/19683=1.038