If `r^(1//3) + 1/(r^(1//3))=3" for a real number " r!=0 ," then what is " r+1/r ` equal to ?

If r is a real number |r| lt 1 and if a= 5(1-r) , then

The radius of nucleus is R=R_(0)A^(1//3) where A is the mass number of the atom. What are the dimensions of R_(0) ?

Let r_(1),r_(2),r_(3) be the three (not necessarily distinct) solution to the equation x^(3)+4x^(2)-ax+1=0. If a can be any real number,then find the minimum value of (r_(1)+(1)/(r_(1)))^(2)+(r_(2)+(1)/(r_(2)))^(2)+(r_(3)+(1)/(r_(3)))^(2)

Let r_1, r_2, r_3 be the three (not necessarily distinct) solution to the equation x^3 + 4x^2 - ax +1 = 0 . If a can be any real number, then find the minimum value of (r_1+1/r_1)^2+(r_2+1/r_2)^2+(r_3+1/r_3)^2 .

If (r)/(r_(2))=(r_(1))/(r_(3)) then