Question

yadi a²=b+c,b²=a+c,c2=b+a hai to a/a+1 +b/b+1 +c/c+1 ka man kya hoga​

Answer 1

Answer:

a² = b + c

b² = c + a

c² = a + b

a² - b² = b - a => (a - b) (a + b) = b - a

=> a + b = -1 or a = b

1) a + b ≠ - 1 as c² is not negative, if c is a real number.

a = b => c² = 2 a

similarly, b = c => a² = 2 b (as b+c ≠ -1, as a² is non negative)

and c = a => b² = 2 a

so we get a = b = c = 2

\begin{gathered}\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\\\\=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1\end{gathered}

1+a

1

+

1+b

1

+

1+c

1

=

3

1

+

3

1

+

3

1

=1