`2^x-2^(x-1)=4, "then" x^x is`

Let f : R to and f (x) = (x (x^(4) + 1) (x+1) +x ^(4)+2)/(x^(2) +x+1), then f (x) is :

The solution set of (x+(1)/(x) ) ^2 -3/2 (x-(1)/(x)) =4 when x ne 0 is

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

The number of real roots of sin (2^x) cos (2^x) =1/4 (2^x+2^-x) is

The number of real roots of sin (2^x) cos (2^x) =1/4 (2^x+2^-x) is

Without expanding, show that the value of each of the determinants is zero: |[(2^x+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|

The function f(x)=(2x^2-1)/x^4, x gt 0 decreases in the interval

If 2x - (1)/(2x) =4 , find : (i) 4x^(2) + (1)/( 4x^2)