Question

If a²÷(b+c)+b²÷(c+a)+c²÷(a+b)=0 then prove that a÷(b+c)+b÷(c+a)+c÷(a+b) = 1​

Answer 1

take a/(b+c) +b/(c+a) +c/(a+b) =1

then multiply (a+b+c) in both the sides
a(a+b+c) / (b+c) + b(a+b+c) / (a+c) + c(a+b+c) / (b+a) = 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) + a + b2 / (c+a) + b + c2 / (a+b) + c = a+b+c

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

Hence Proved

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Answer 2

Step-by-step explanation:

If a²÷(b+c)+b²÷(c+a)+c²÷(a+b)=0 then prove that a÷(b+c)+b÷(c+a)+c÷(a+b) = 1