Question

If a+b+c=0, show that
${x}^{ {a}^{2} {b}^{ - 1} {c}^{ - 1} } \times {x}^{ {b}^{2} {a}^{ - 1} {c}^{ - 1} } \times {x}^{ {c}^{2} {a}^{ - 1} {b}^{ - 1} } = {x}^{3}$
​

Answer 1

Answer:

Let Z=X

a

2

b

−1

c−1

X

a

−1

b

2

c

−1

X

a

−1

b

−1

c

2

⇒Z=X

bc

a

2

+

ac

b

2

+

ab

c

2

⇒

bc

a

2

+

ac

b

2

+

ab

c

2

=

abc

a

3

+b

3

+c

3

=

abc

3abc

=3 ....[a+b+c=0]

⇒Z=X

3