Question

resolva a inequação √2x>x²

Answer 1

$\sqrt{2x} >x^2\\ \\ \sqrt2.\sqrt x>x^2\\ \\ \sqrt2<\frac{x^2}{\sqrt x}\\ \\ \frac{x^2}{x^{\frac{1}{2}}}>\sqrt2\\ \\ x^{2-\frac{1}{2}}>\sqrt2\\ \\ x^{\frac{3}{2}}>\sqrt2\\ \\ (x^{\frac{3}{2}})^{\frac{2}{3}}<(2^{\frac{1}{2}})^{\frac{2}{3}}\\ \\ x<2^{\frac{2}{3}}\\ \\ \boxed{x< \sqrt[3]{2} }$

Como x>0 temos:

[tex]\boxed{S=\{x \in R/0