# Find a+b+c

#### anemone

##### MHB POTW Director
Staff member
The real root of the equation $$\displaystyle 8x^3-3x^2-3x-1=0$$ can be written in the form $$\displaystyle \frac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}$$, where $$\displaystyle a,\;b,\,c$$ are positive integers.

Find $$\displaystyle a+b+c$$.

#### mathworker

##### Well-known member
$$\displaystyle 8x^3-3x^2-3x-1=0$$
$$\displaystyle 9x^3=(x+1)^3$$
$$\displaystyle 9=(1+\frac{1}{x})^3$$
$$\displaystyle x=\frac{1}{\sqrt[3]{9}-1}$$
by factorizing,
$$\displaystyle a=81,b=9,c=8$$
$$\displaystyle a+b+c=98$$

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