Question

a/(b+c)+b/(c+a)+c/(a+b)=1 then prove that a*a/(b+c)+b*b/(c+a)+c*c/(a+b)=0

Answer 1

LET A/B+C=-1,B/C+A=1,C/A+B=1 will satisfy this equation

 

from above,

a= -(b+c),......(1)

b=c+a.....(2)

c=a+b.....(3)

 

now adding equation1,2,3

a+b+c=2a

b+c=a....(4)

 

now a2/b+c=a*(a/b+c)=-a......(5)

 

similarly b2/c+a=b...............(6)

aand

c2/a+b=c.......(7)

 

 

now adding equaation5,6,7

we find desire value

(a2/b+c)+( b2/c+a)+(c2/a+b)=-a+b+c...(8)

 

from equaation 4

b+c=a

 

put value inequation 8

-a+b+c= -a+a=0

 

hence proved

Answer 2

Answer:

Step-by-step explanation:

(a+b+2ac) (a-2b) hope it helps :)