Question

If a, b, c are all non zero and a+b+c=0, prove that a²/bc + b²/ca + c²/ab = 3

Answer 1

Answer:

Step-by-step explanation:

Brainly User

Hey

Given that :-

a + b + c = 0 .

To prove :-

a² / bc + b² / ca + c² / ab = 3

Proof :-

a² / bc + b² /ca + c² / ab

=a³ + b³ + c³ / abc

NoTe :- Formulae to be used = when ( a + b + c = 0 ) then ( a³ + b³ + c³ = 3abc ) .

Now ,

putting value of ( a³ + b³ + c³ )

= 3abc / abc

= 3 .

♦ PROVED ♦

thanks :)

Answer 2

Answer

Let's simplify the given equation first:

$\frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ca} + \frac{ {c}^{2} }{ab} \\ \\ = > \frac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc}$

We know an identity:

When: a + b + c = 0;

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

Applying the same here:

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