MathDB

8

Part of 2017 QEDMO 15th

Problems(2)

exists triangle of medians (15th -a QEDMO p8 19. - 22. 10. 2017)

Source:

5/30/2021
Let ABCABC be a triangle of area 11 with medians sa,sb,scs_a, s_b,s_c. Show that there is a triangle whose sides are the same length as sa,sbs_a, s_b, and scs_c, and determine its area.
geometryMedianstriangle inequality
f (-42)=? if f (x^2 + yf (z)) = xf (x) + zf (y) , (2017)> 0

Source: 15th -b QEDMO problem 8 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

5/30/2021
For a function f:R→Rf: R\to R , f(2017)>0 f (2017)> 0 as well as f(x2+yf(z))=xf(x)+zf(y)f (x^2 + yf (z)) = xf (x) + zf (y) for all x,y,z∈Rx,y,z \in R is known. What is the value of f(−42)f (-42)?
algebrafunctionalfunctional equation