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Math Help - Please help solve inequalities

  1. #1
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    Question Please 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!
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  2. #2
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    Krizalid's Avatar
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    Quote Originally Posted by live_laugh_luv27 View Post

    Solve the inequality:

    1. x^2 - (2/x) > 0
    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 x^{2}+\sqrt[3]{2}x+\sqrt[3]{4}>0, you just need to solve \frac{x-\sqrt[3]{2}}{x}>0.

    Quote Originally Posted by live_laugh_luv27 View Post

    2. (x-5)^4 / (x(x+3)) ≥ 0
    Numerator is always positive (and zero when x=5), so, you just need to solve x(x+3)>0.
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  3. #3
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    Thanks for your help, I really appreciate it!
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