Grade 12th passAlgebra

if a2/(b+c)=b2/(c+a)=c2/(a+b)=1, then 1/(1+a)+1/(1+b)+1/(1+c)=1

sulagna

8 Years agoGrade 12th pass

2 Answers

Meet

8 Years ago

As if u solve the equation in 3 variable then u will get that a=2,b=2,c=2. and now if u put these values in 2nd equation then it will become 1/3+1/3+1/3=1 hence proved

mycroft holmes

8 Years ago

$a^2=b+c \Rightarrow a^2+a = a(1+a) = a+b+c \Rightarrow \dfrac{1}{1+a} = \dfrac{a}{a+b+c}$

Similarly $\dfrac{1}{1+b} = \dfrac{b}{a+b+c}$ and $\dfrac{1}{1+c} = \dfrac{c}{a+b+c}$

Hence $\dfrac{1}{1+a}+ \dfrac{1}{1+b}+ \dfrac{1}{1+c} = \dfrac{a}{a+b+c}+ \dfrac{b}{a+b+c}+\dfrac{c}{a+b+c}$

$\dfrac{a+b+c}{a+b+c}=1$

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