MathDB

4

Part of 2003 APMO

Problems(1)

In ineqaulity with sides of triangle

Source: APMO 2003

3/5/2006
Let a,b,ca,b,c be the sides of a triangle, with a+b+c=1a+b+c=1, and let n≥2n\ge 2 be an integer. Show that an+bnn+bn+cnn+cn+ann<1+2n2. \sqrt[n]{a^n+b^n}+\sqrt[n]{b^n+c^n}+\sqrt[n]{c^n+a^n}<1+\frac{\sqrt[n]{2}}{2}.
inequalities