Question

गोलगीकाय ने कोषनीआत्माघाती कोथङो कहे छे। सहि हे या गलत। ​

Answer 1

QUESTION:-

$\sf\therefore \dfrac{(b+c)^2}{bc} + \dfrac{(c+a)^2}{ca} + \dfrac{(a+b)^2}{ab}$

$\sf\large\therefore note:-question\:is\:incorrect$

CORRECT QUESTION,

$\sf{\text{If \:a+b+c =0\: then\: show ,}}$

$\bf\therefore \frac{(b+c)^2}{bc} + \frac{(c+a)^2}{ca} + \frac{(a+b)^2}{ab}$

ANSWER✔

$\Large\underline\bold{GIVEN,}$

$\sf\implies a + b + c=0.$

$\sf\implies a + b = -c$

$\sf\implies a + c = -a$

$\sf\implies c + a = -1$

$\Large\underline\bold{TO\:PROVE,}$

$\sf\large\therefore \frac{(b+c)^2}{bc} + \frac{(c+a)^2}{ca} + \frac{(a+b)^2}{ab}$

$\Large\underline\bold{SOLUTION,}$

$\sf\therefore Taking \:LHS,$

$\sf\large\implies \frac{(b+c)^2}{bc} + \frac{(c+a)^2}{ca} + \frac{(a+b)^2}{ab}$

$\sf\large\therefore substituting \:the \:value\: of \:eq. \:1,2,3$

$\sf\large\implies \frac{(-a)^2}{bc} + \frac{(-b)^2}{ca} + \frac{(-c)^2}{ab}$

$\sf\large\implies \frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}$

$\sf\therefore taking\:LCM,$

$\sf\large\implies \frac{a^3+b^3+c^3}{abc}$

$\sf\therefore we\:know$

$\sf\large\implies (a+b+c)=0 , a^3+b^3+c^3=3abc$

$\sf\large\implies \frac{3abc}{abc}$

$\sf\large\implies RHS=3$

$\large{\boxed{\sf{RHS=3}}}$

HENCE,R.H.S =3