MathDB

1

Part of 2011 Greece JBMO TST

Problems(1)

2\sqrt {x-1} +4\sqrt {y-4} + 6\sqrt {z-9} = x+y+z

Source: Greece JBMO TST 2011 p1

4/29/2019
a) Let nn be a positive integer. Prove that nx−n2≤x2 n\sqrt {x-n^2}\leq \frac {x}{2} , for x≥n2x\geq n^2. b) Find real x,y,zx,y,z such that: 2x−1+4y−4+6z−9=x+y+z 2\sqrt {x-1} +4\sqrt {y-4} + 6\sqrt {z-9} = x+y+z
Inequalityequationalgebra