If `x,y,zepsilonR` then the value of `|((2x^(x)+2^(-x))^(2),(2^(x)-2^(-x))^(2),1),((3x^(x)+3^(-x))^(2),(3^(x)-3^(-x))^(2),1),((4^(x)+4^(-x))^(2),(4^(x)-4^(-x))^(2),1)|` is

|[2^(x)-2^(-x))^(2),(2^(x)+2^(-x))^(2),1(3^(x)-3^(-x))^(2),(3^(x)+3^(-x))^(2),1(4^(x)-4^(-x))^(2),(4^(x)+4^(-x))^(2),1]

If x,y,z in R , then the value of determinant |{:((2^x+2^(-x))^2,(2^x-2^(-x))^2,1),((3^x+3^(-x))^2,(3^x-3^(-x))^2,1),((4^x+4^(-x))^2,(4^x-4^(-x))^2,1):}| is equal to "............"

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]|

y=(x+1)^(2)(x+2)^(3)(x+3)^(4)

If x-(1)/(x)=1 , then the value of (x^(4)-(1)/(x^(2)))/(3x^(2)+5x-3) is

If x^(4) - 3x^(2) - 1 = 0 , then the value of (x^(6)-3x^(2)+(3)/(x^(2))-(1)/(x^(6))+1) is :

int(x^(4)-2x^(2)+4x+1)/(x^(3)-x^(2)-x+1)dx

Solve for x:4^(x)-3^(x-1/2)=3^(x+1/2)-2^(2x-1)