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If x/b+c=y/c+a=z/a+b then show that (b-c)x+(c-a)y+(a-b)z=0

If x/b+c=y/c+a=z/a+b then show that (b-c)x+(c-a)y+(a-b)z=0

Grade:12th pass

1 Answers

Arun
25750 Points
4 years ago
Dear student
 
Let x/b+c=y/c+a=z/a+b = k
then
x=(b+c)k        ...(1)
y=(c+a)k        ...(2)
z=(a+b)k        ...(3)
to prove
(b-c) x+(c-a) y+(a-b) z=0
L.H.S. = (b-c) x+(c-a) y+(a-b) z
= (b-c) (b+c) k + (c-a) (c+a)k + (a-b) (a+b)k                  by eq (1), (2) & (3)
= k [(b-c) (b+c)  + (c-a) (c+a) + (a-b) (a+b) ]
=k[b^2 – c^2 + c^2 – a^2 + a^2 – b^2]
= k [0]
= 0
 
Hope it helps

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