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Show-that-for-all-real-values-of-x-x-2-3-6x-1-3-10-gt-0-




Question Number 66399 by Rio Michael last updated on 14/Aug/19
Show that for all real  values of x;     x^(2/3)  + 6x^(1/3)  + 10 >0
$${Show}\:{that}\:{for}\:{all}\:{real} \\ $$$${values}\:{of}\:{x};\: \\ $$$$\:\:{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:+\:\mathrm{6}{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:\mathrm{10}\:>\mathrm{0} \\ $$
Commented by kaivan.ahmadi last updated on 14/Aug/19
=(x^(1/3) +3)^2 +1>0
$$=\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{3}\right)^{\mathrm{2}} +\mathrm{1}>\mathrm{0} \\ $$$$ \\ $$

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