Question

1/b+c+1/c+a=2/a+b than prove a2+b2=2c2​

Answer 1

hope this help.............

Answer 2

a² + b² = 2c² (Proved)

Step-by-step explanation:

Given,

$\frac{1}{b+c} + \frac{1}{c+a} = \frac{2}{a+b}\\=> \frac{c+a+b+c}{(b+c)(c+a)}=\frac{2}{a+b}\\=> \frac{2c+a+b}{bc+ab+c^{2}+ac}=\frac{2}{a+b}$

Now, cross multiply,

=> (2c + a + b)(a + b) = 2(bc + ab + c² + ac)

=> 2ac + 2bc + a² + ab + ab + b² = 2bc + 2ab + 2c² + 2ac

=> 2ac + 2bc + a² + 2ab + b² = 2bc + 2ab + 2ac + 2c²

=> a² + b² = 2c² +2bc - 2bc + 2ab - 2ab + 2ac - 2ac

=> a² + b² = 2c²

Hence, a² + b² = 2c² (Proved)