Question

If a+1/b=b+1/c=c+1/c .then find out the value of a^2*b^2*c^2​

Answer 1

Step-by-step explanation:

Answer

Δ=

∣

∣

∣

∣

∣

∣

∣

∣

a

1

a

2

a

3

b

1

b

2

b

3

c

1

c

2

c

3

∣

∣

∣

∣

∣

∣

∣

∣

⇒Δ=a

1

(b

2

c

3

−b

3

c

2

)+b

1

(a

3

c

2

−a

2

c

3

)+c

1

(a

2

b

3

−a

3

b

2

)

We have to find

∣

∣

∣

∣

∣

∣

B

2

B

3

C

2

C

3

∣

∣

∣

∣

∣

∣

Here, B

2

is cofactor of element b

2

So, B

2

=

∣

∣

∣

∣

∣

∣

a

1

a

3

c

1

c

3

∣

∣

∣

∣

∣

∣

⇒B

2

=a

1

c

3

−a

3

c

1

C

2

is cofactor of element c

2

So, C

2

=−

∣

∣

∣

∣

∣

∣

a

1

a

3

b

1

b

3

∣

∣

∣

∣

∣

∣

⇒C

2

=a

3

b

1

−a

1

b

3

B

3

is cofactor of element b

3

So, B

3

=−

∣

∣

∣

∣

∣

∣

a

1

a

2

c

1

c

2

∣

∣

∣

∣

∣

∣

⇒B

3

=a

2

c

1

−a

1

c

2

C

3

is cofactor of element c

3

So, C

3

=

∣

∣

∣

∣

∣

∣

a

1

a

2

b

1

b

2

∣

∣

∣

∣

∣

∣

⇒C

3

=a

1

b

2

−a

2

b

1

Now,

∣

∣

∣

∣

∣

∣

B

2

B

3

C

2

C

3

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

a

1

c

3

−a

3

c

1

a

2

c

1

−a

1

c

2

a

3

b

1

−a

1

b

3

a

1

b

2

−a

2

b

1

∣

∣

∣

∣

∣

∣

=a

1

2

b

2

c

3

−a

1

a

2

b

1

c

3

−a

1

a

3

b

2

c

1

−a

1

2

b

3

c

2

+a

1

a

2

b

3

c

1

+a

1

a

3

b

1

c

2

=a

1

[a

1

(b

2

c

3

−b

3

c

2

)+b

1

(a

3

c

2

−a

2

c

3

)+c

1

(a

2

b

3

−a

3

b

2

)]

=a

1

Δ

Answer 2

Answer:

please refer to the image