For `a gt 0` , least possible value of expression
`E=a+2a^2+a^3+1/a+1/a^3+1/a^4` is

The least value of expression 2 log_(10)x - log_(x) (1//100) for x gt 1 is:

If a gt 0 , the least value of (a^3+a^2+a+1)^2 is

If (x - 3)(2x + 1) = 0, then the possible values of 2x + 1 are:

If x in R - {0} then minimum possible value of the expression (1)/(7)[(3x^(2)+(4)/(3x^(2))+1)^(2)-2(3x^(2)+(4)/(3x^(2)))+4]

if x^(2)+y^(2)-4x-6y-3=0, then minimum possible value of the expression 16[(1)/((x-2)^(2))+(1)/((y-3)^(2))] is equal to:

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

If a,beta in R satisfies a^(2)+beta^(2)-2a+6 beta+1=0 then least possible value of a^(2)+beta^(2)-2a-4 beta is