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If A/(B + C) = B/(C + A) = C/(A + B) , Then Prove that A(B - C) + B(C-a) + C (A - B) = 0 - ICSE Class 10 - Mathematics

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Question

If `"a"/("b + c") = "b"/("c + a") = "c"/("a + b")` , then prove that a(b - c) + b(c-a) + c (a - b) = 0

Solution

`"a"/("b + c") = "b"/("c + a") = "c"/("a + b") = "k"`

a = k(b + c) 

b = k(c+a) 

c= k(a+b) 

a (b - c)+ b (c - a)+ c (a - b) = 0 

LHS 

a (b - c)+ b (c - a)+ c (a - b) 

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

= k(b2 - C2) + k( c2 - a2) + k( a2 - b2

= kb2 - kc2 + kc2 - ka2 + ka2 - kb2  

= 0 = RHS

LHS = RHS. Hence, proved. 

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 12

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Solution If A/(B + C) = B/(C + A) = C/(A + B) , Then Prove that A(B - C) + B(C-a) + C (A - B) = 0 Concept: Ratio and Proportion Example.
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