If x^2+1/x=18 then find The value of x minus 1/x

Hello.

Multiply all terms by x and cancel:

x2x+1=18x

x3+1=18x (Simplify both sides of the equation)

x3+1-18x=18x-18x (Subtract 18x from both sides)

x3-18x+1=0

(Use cubic formula)

x=-4.27015,0.055565,4.214585

Check answers. (Plug them in to make sure they work.)

x=4.214585 (Works in original equation)

x=-4.27015 (Works in original equation)

x=0.055565 (Works in original equation)

So the answer is: 4

Have a nice day