If `x=(5-sqrt(21))/2` then prove that `(x^3+1/x^3)-5(x^2+1/x^2)+(x+1/x)=0`

If x = (5-sqrt(21))/2 , find the value of x+(1)/(x)

If x=(5-sqrt(21))/(2), then the value of (x^(3)+(1)/(x^(3)))^(2)-5(x^(2)+(1)/(x^(2)))+(x+(1)/(x))

If x=(sqrt(2)+1)^(-1/3) , then prove that (x-x^(-1))^3+3(x-x^(-1))+2=0 .

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

Prove that |(1,x,x^2),(x^2,1,x),(x,x^2,1)|=(1-x^2) .

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0

If y = [ x + 5 + sqrt(x^2 + 10x + 1)]^n then prove that (x^2 + 10x + 1) y_2 + (x + 5) y_1 - n^2y = 0 .

If f(x)= 2x^2+3x+5 , then prove that f'(0)+3f'(-1)=0

If x=(1)/(sqrt(5)-2) , find the value of x^(3)-3x^(2)-5x+3 .