Question

please solve this question​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

We know

$\tt \: If \: a \: + \: b \: + \: c \: = \: 0$

then

$\tt \: {a}^{3} + {b}^{3} + {c}^{3} = 3abc$

Now,

$\tt \: \dfrac{ {a}^{2} }{bc} + \dfrac{ {b}^{2} }{ca} + \dfrac{ {c}^{2} }{ab}$

$\tt \: = \dfrac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc}$

$\tt \: = \dfrac{3abc}{abc}$

$\tt \: = 3$

$\boxed{ \red{ \bf \: option \: (d) \: is \: correct}}$

Answer 2

Solution:−

We know

\tt \: If \: a \: + \: b \: + \: c \: = \: 0Ifa+b+c=0

then

\tt \: {a}^{3} + {b}^{3} + {c}^{3} = 3abca

3

+b

3

+c

3

=3abc

Now,

\tt \: \dfrac{ {a}^{2} }{bc} + \dfrac{ {b}^{2} }{ca} + \dfrac{ {c}^{2} }{ab}

bc

a

2

+

ca

b

2

+

ab

c

2

\tt \: = \dfrac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc}=

abc

a

3

+b

3

+c

3

\tt \: = \dfrac{3abc}{abc}=

abc

3abc

=3