The minimum value of `((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^3)` is (for x>o)

The minimum value of x^3-6x^2+9x+1 is

Minimum value of ((1+x^(2))(1+x^(6)))/(x^(4)) is

x^(3)-(1)/(x^(3))-6x+(6)/(x)

(x^3+1/x^3)+(x^2+1/x^2)-6(x+1/x)-7=0

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

((1)/(x-3)-(3)/(x(x^(2)-5x+6)))

If x=(6-sqrt(32))/(2), then find the value of (x^(3)-(1)/(x^(3)))^(2)-6(x^(2)+(1)/(x^(2)))+(x+(1)/(x))

(2(x-3))/(x(x-6))<=(1)/(x-1)

Evaluate: int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3))).dx