MathDB

A5

Part of 2018 JBMO Shortlist

Problems(1)

0<= a,b,c,d<=1<=x,y,z,t and a+b+c+d +x+y+z+t=8 show sum of squares<=28

Source: JBMO Shortlist 2018 A5

7/22/2019
Let a,b,c,d,b,c,d and x,y,z,tx,y,z,t be real numbers such that 0≤a,b,c,d≤10\le a,b,c,d \le 1 , x,y,z,t≥1x,y,z,t \ge 1 and a+b+c+d+x+y+z+t=8a+b+c+d +x+y+z+t=8. Prove that a2+b2+c2+d2+x2+y2+z2+t2≤28a^2+b^2+c^2+d^2+x^2+y^2+z^2+t^2\le 28
algebrainequalities