Solve the inequality:

1. x^2 - (2/x) > 0

2. (x-5)^4 / (x(x+3)) ≥ 0

Thank you for any help!

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- Nov 30th 2008, 08:40 AMlive_laugh_luv27Please help solve inequalities
Solve the inequality:

1. x^2 - (2/x) > 0

2. (x-5)^4 / (x(x+3)) ≥ 0

Thank you for any help! - Nov 30th 2008, 09:21 AMKrizalid
$\displaystyle x^{2}-\frac{2}{x}=\frac{x^{3}-2}{x}=\frac{\left( x-\sqrt[3]{2} \right)\left( x^{2}+\sqrt[3]{2}x+\sqrt[3]{4} \right)}{x}>0,$ and since $\displaystyle x^{2}+\sqrt[3]{2}x+\sqrt[3]{4}>0,$ you just need to solve $\displaystyle \frac{x-\sqrt[3]{2}}{x}>0.$

Numerator is always positive (and zero when $\displaystyle x=5$), so, you just need to solve $\displaystyle x(x+3)>0.$ - Nov 30th 2008, 09:24 AMlive_laugh_luv27
Thanks for your help, I really appreciate it!