Math, asked by mailsarkaranurpd8od2, 1 year ago

if a2= b+c, b2= c+a, c2= a+b, then find the value of 1/1+a+1/1+b+1/1+c

Answers

Answered by opriyanka305
32
1/1+a+1/1+b+1/1+c
=a/a+a²+b/b+b²+c/c+c²
=a/a+b+c + b/a+b+c + c/a+b+c
=a+b+c/a+b+c
=1
value is 1
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Answered by guptasingh4564
33

Thus, The value of  \frac{1}{1+a} +\frac{1}{1+b} +\frac{1}{1+c}  is 1

Step-by-step explanation:

Given;

a^{2}=b+c , b^{2}=c+a , c^{2} =a+b then \frac{1}{1+a} +\frac{1}{1+b} +\frac{1}{1+c} =?

\frac{1}{1+a} +\frac{1}{1+b} +\frac{1}{1+c}

=\frac{a}{a(1+a)} +\frac{b}{b(1+b)} +\frac{c}{c(1+c)}

=\frac{a}{a+a^{2} } +\frac{b}{b+b^{2} } +\frac{c}{c+c^{2} }

Plug a^{2} , b^{2} and c^{2} value in above equation;

=\frac{a}{a+b+c } +\frac{b}{b+a+c } +\frac{c}{c+a+b}

=\frac{a+b+c}{a+b+c }

=1

∴ The value of  \frac{1}{1+a} +\frac{1}{1+b} +\frac{1}{1+c}  is 1

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