If `a=sqrt2+1`, then `a^3+1/a^3=?`

If x^(2)+1=sqrt(3)x, then (x^(3)+(1)/(x^(3)))^(2n+1) for any n in N is equal to

If x=(2+sqrt(3))^((1)/(3)) then x^(3)+(1)/(x^(3))=

If sqrt(2)=1.414,sqrt(3)=1.732 , find the value of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)" "(ii)(sqrt(3)-1)/(sqrt(3)+1)" "(iii)(2+sqrt(6))/(sqrt(2))

Determine the value of ............... (1)/(sqrt1 +sqrt2) +(1)/(sqrt2 + sqrt3) +(1)/(sqrt3 + sqrt4) + ……+ (1)/(sqrt120 + sqrt121)

Evaluate : 1/( 1 + sqrt (2) ) + 1/( sqrt(2) + sqrt (3) ) + 1/ ( sqrt(3) + sqrt (4) )