Question

if a(y+z)=b(z+x)=c(x+y) and out of A,B,C no two of them are equal than show that y-z/a(b-c)=z-x/b(c-a)=x-y/c(a-b)

Answer 1

a(y+z)=b(z+x)=c(x+y) 

Assume n= a(y+z)=b(z+x)=c(x+y) 

n=a(y+z) ,n= b(z+x) , n= c(x+y) 

y+z = (n/a).....................(1) 

z+x = (n/b).....................(2) 

x+y = (n/c).....................(3) 

subtracting (2) - (1) , (3) - (2) , (1) - (3) we get 

x - y = n( a - b )/ab ..................(4) 

y - z = n ( b - c )/bc...................(5) 

z - x = n( c - a )/ac...................(6) 


x-y/c(a-b) = [ n ( a - b )/ab ] / c( a - b ) 
= n/abc 

y-z/a(b-c) = [ n ( b - c )/bc ] / a( b - c ) 
= n/abc 

z-x/b(c-a) = [ n ( c - a )/ac ] / b( c - a ) 
= n/abc 

y-z/a(b-c)=z-x/b(c-a)=x-y/c(a-b)

Answer 2

STEP BY STEP EXPLANATION