Let `x_1,x_2` be two positive real numbers. Statement - 1: The minimum value of `(16/(x_1^ 2)+(y_1^ 2)/2+(x_1^ 2)/(y_1^ 2)) is 2` Statement - 2: `(x_1+x_2)/2 >= sqrt(x_1 x_2).`

If x is real, then the minimum value of y=(x^(2)-x+1)/(x^(2)+x+1) is

Let x , y be two variables and x >0, x y=1 , then minimum value of x+y is (a) 1 (b) 2 (c) 2 1/2 (d) 3 1/3

Let x ,\ y be two variables and x >0,\ \ x y=1 , then minimum value of x+y is (a) 1 (b) 2 (c) 2 1/2 (d) 3 1/3

Find the minimum value of (x_1-x_2)^2+(sqrt(2-x_1^2)-9/(x_2))^2 where x_1in(0,sqrt2) and x_2inR^+

Find the minimum value of (x_1-x_2)^2+((x_1^2)/20-sqrt((17-x_2)(x_2-13)))^2 where x_1 in R^+,x_2 in (13,17) .

Find the minimum value of (x_1-x_2)^2+((x_1^2)/20-sqrt((17-x_2)(x_2-13)))^2 where x_1 in R^+,x_2 in (13,17) .

Find the minimum value of (x_1-x_2)^2+((x_1^2)/20-sqrt((17-x_2)(x_2-13)))^2 where x_1 in R^+,x_2 in (13,17) .

If x,y,z are distinct real numbers then the value of ((1)/(x-y))^(2)+((1)/(y-z))^(2)+((1)/(z-x))^(2) is

Minimum value of (x_(1)-x_(2))^(2)+(sqrt(2-x_(1)^(2))+x_(2)-8)^2 ,where x_(1)in[-sqrt(2),sqrt(2)] and x_(2)in R is

Consider the function f(x)=(1)/(2{-x})-{x} where {x} denotes the fractional part of x and x is not an integer.Statement-1: The minimum value of f(x) is sqrt(2)-1 statement-2: Ifthe product of two positive numbers is a constant then minimum 2 xx the square root of their product.