Question

algebra question.....plz help me with this question

Answer 1

as simple as that.

step 1 use componendo and dividendo.

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

so 3 equations are given.

just use componendo and dividendo in these

componendo dividendo means.

if a c a + b c + d
--- = --- then -------- = --------
b d a - b c - d

so apply this on these 3 equation.

a + b - c - ( a + b ) b + c - a - ( b +c )
------------------------ = ------------------------ =
a + b - c + ( a + b ) b + c - a + ( b + c )


c + a - b - ( c + a )
--------------------------
c + a - b + ( c + a )


so simplify now.

-c -a -b
-------------- = ---------------- = ---------------
2a + 2b - c 2b + 2c - a 2c + 2a -b

hence denominator is equal and numerator are also equal and hence

a = b = c

hence proved :)

I hope it helps