solve-for-x-if-3-2-1-x-3-

Question Number 44212 by 12344 last updated on 23/Sep/18

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{if}. \\ $$$$\mathrm{3}^{\mathrm{2}} −\mathrm{1}=\mathrm{x}^{\mathrm{3}} \\ $$

Answered by Joel578 last updated on 23/Sep/18

$$\mathrm{9}\:−\:\mathrm{1}\:=\:{x}^{\mathrm{3}} \\ $$$${x}^{\mathrm{3}} \:=\:\mathrm{8} \\ $$$${x}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{8}}\:=\:\mathrm{2} \\ $$

Commented by MJS last updated on 23/Sep/18

x^3 −8=0 (x−2)(x^2 +2x+4)=0 x_1 =2 x_2 =−1−i(√3) x_3 =−1+i(√3)

$${x}^{\mathrm{3}} −\mathrm{8}=\mathrm{0} \\ $$$$\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =\mathrm{2} \\ $$$${x}_{\mathrm{2}} =−\mathrm{1}−\mathrm{i}\sqrt{\mathrm{3}} \\ $$$${x}_{\mathrm{3}} =−\mathrm{1}+\mathrm{i}\sqrt{\mathrm{3}} \\ $$