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Grade: 12th pass
        if a/b+c+b/c+a+c/a+b=1 then find a*a/b+c+b*b/c+a+c*c/a+b
9 months ago

Answers : (1)

Arun
13861 Points
							

Given relation

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

Multiplying both sides by a+b+c we get (a+b+c!=0)

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

a2b+c+a(b+c)b+c+b2c+a+b(c+a)c+a+c2a+b+c(a+b)a+b=(a+b+c)=>a^2/(b+c)+(a(b+c))/(b+c)+b^2/(c+a)+(b(c+a))/(c+a)+c^2/(a+b)+(c(a+b))/(a+b)=(a+b+c)

a2b+c+a+b2c+a+b+c2a+b+c=(a+b+c)=>a^2/(b+c)+a+b^2/(c+a)+b+c^2/(a+b)+c=(a+b+c)

=>a^2/(b+c)+b^2/(c+a) + c^2/(a+b) = 0

Regards

Arun (askIITians forum expert)

9 months ago
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