Question

If
$\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} = 1$
Then find
$\frac{ {a}^{2} }{b + c} + \frac{ {b}^{2} }{c + a} + \frac{ {c}^{2} }{a + b} = ........$
A) 0
B) 1
C)2
D)3

(EXAM CPO 2012)

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Answer 1

a/(b + c) + b/(c + a) + c/(a + b) = 1
multiple both sides with (a + b+ c)

a(a + b + c)/(b+c) + b(a + b + c)/(c + a) + c(a + b + c)/(a + b) = (a + b + c)

a²/(b + c) + a(b+c)/(b+c) + b²/(c + a) + b(c + a)/(c + a) + c²/(a + b) + c(a+b)/(a + b)
= (a + b + c)

a²/(b + c) + b²/(c + a ) + c²/(a + b ) + (a + b+ c ) = (a + b + c )

a²/(b + c ) + b²/(c + a) + c²/(a + b) = 0

hence, option ( A ) is correct