Question

x + y + z = varies (x + z - y)(x + y - z) varies yz prove y+z-x =yz

Answer 1

Answer:

According to question

sum of x,y,z is constant

Let x+y+z=k

(z+x-2y)(x+y-2z)∝yz

→(k−y−2y)(k−z−2z)∝yz

→(k−3y)(k−3z)∝yz

→k

2

−3k(y+z)+9yz=myz

where m is proportionality constant

→−k(3(y+z)−k)=(m−9)yz

→(3(y+z)−x−y−z)=−

k

(m−9)yz

∴(2y+2z−x)=

k

(9−m)yz

→(2(y+z)−x)∝yz

where

k

9−m

= constant