Prove that \(\frac {1}{2} (x^2 + y^2) \geq xy\) for any \(x\) and \(y\).
Prove that for \(x \geq 0\) the inequality is valid: \(2x + \frac {3}{8} \ge \sqrt[4]{x}\).
We can define the absolute value \(|x|\) of any real number \(x\) as follows. \(|x|=x\) if \(x\ge0\) and \(|x|=-x\) if \(x<0\). What are \(|3|\), \(|-4.3|\) and \(|0|\)?
Prove that \(|x|\ge0\).