Question

if a+b+c=0 , proce that a²/bc+b²/ab+c²/ca=3​

Answer 1

Answer:

It is given that $a+b+c = 0$

We must prove that $\frac{a^{2} }{bc} +\frac{b^{2}}{ab} + \frac{c^{2}}{ac} = 3$

$L.C.M(ab,bc,ca) = abc$

⇒ $\frac{a^{3} +b^{3}+c^{3}}{abc} = 3$

We know that $a^{3} + b^{3} +c^{3} = 3abc$ if $a+b+c = 0$

⇒ $\frac{3abc}{abc} = 3$

⇒ $3=3$

⇒ $L.H.S=R.H.S$

∴ $\frac{a^{2} }{bc} +\frac{b^{2}}{ab} + \frac{c^{2}}{ac} = 3$ if $a+b+c = 0$