+179 Find the largest positive real number \(\lambda\) such that for any nonnegative real numbers x, y, and z such that x^2 + y^2 + z^2 = 1, the inequality
\(\lambda xy + yz \le \frac{\sqrt{5}}{2}\) holds.
Thank you for any help!
+171 i asked one person i know about this one, as for me myself am not sure, and he said his first impression was to do $ y(\lambda x +z) \le \sqrt{\frac{5}{2}} $
$ y \le\frac{\sqrt{\frac{5}{2}} }{(\lambda x +z)} $
any idea what to do next?
