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

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