# How do you factor and solve b^2-\frac{5}{3b}=0?

Nov 1, 2014

${b}^{2} - \frac{5}{3 b} = 0$

by multiplying by $b$,

$\implies {b}^{3} - \frac{5}{3} = 0$

by $\frac{5}{3} = {\left(\sqrt[3]{\frac{5}{3}}\right)}^{3}$,

$\implies {b}^{3} - {\left(\sqrt[3]{\frac{5}{3}}\right)}^{3} = 0$

by $\left({a}^{3} - {b}^{3}\right) = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$,

$\implies \left(b - \sqrt[3]{\frac{5}{3}}\right) \left[{b}^{2} + \sqrt[3]{\frac{5}{3}} b + {\left(\sqrt[3]{\frac{5}{3}}\right)}^{2}\right] = 0$

since ${b}^{2} + \sqrt[3]{\frac{5}{3}} b + {\left(\sqrt[3]{\frac{5}{3}}\right)}^{2} \ne 0$,

$\implies b - \sqrt[3]{\frac{5}{3}} = 0 \implies b = \sqrt[3]{\frac{5}{3}}$

I hope that this was helpful