The minimum value of the expression `3^(x)+3^(-1-x),x in R` is `a sqrt(b)` then `a+ b=`( where `a, b` are in lowest form)

If x in R, find the minimum value of the expression 3^(x)+3^(1-x)

The minimum value of (x-a)(x-b) is

The minimum value of the expression x^(3)(x^(3)+1)(x^(3)+2)(x^(3)+3), is ( x in RR )

Let f(b) be the minimum value of the expression y=x^(2)-2x+(b^(3)-3b^(2)+4)AA x in R . Then, the maximum value of f(b) as b varies from 0 to 4 is

If b>a, find the minimum value of |(x-a)^(3)+|(x-b)^(3)|,x in R

If x,y(x!=1) satisfy both the equation 2^(lnx) = 3^(lny) and (ln^2 x) = (ln^3y). The value of the expression sqrt(lny)+3sqrt(lnx) can be expressed as log_b a (where a, b in N). Then find the smallest value of |a-b|.

If the value of the expression sin25^(@)*sin35^(@)*sin85^(@) can be expressed as (sqrt(a)+sqrt(b))/(c) where a,b,cN and are in their lowest form,find the value of (a+b+c)

If the value of the expression tan((1)/(2)cos^(-1).(2)/(sqrt5)) is in the form of a+sqrtb where a, b in Z , then the value of (a+b)/(b) is