Test Index

AFCAT Model Paper 10

© examsnet.com

Question : 51 of 100

Marks: +1, -0

What is the value of the expression?

\frac{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}{3(a-b)(b-c)(c-a)}=?

4
1
2
0

Solution:

Formula Used:

x^{3}+y^{3}+z^{3}-3 x y z = (x+y+z)(x^{2}+y^{2}+z^{2}-x y - y z - z x)

x^{3}+y^{3}+z^{3}=3 x y z

, when

x+y+z=0

Calculation:

Let x = a – b, y = b – c and z = c – a

Now,

⇒ x + y + z = a – b + b – c + c – a

⇒ x + y + z = 0

⇒

x^{3}+y^{3}+z^{3}=3 x y z

⇒

\frac{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}{3(a-b)(b-c)(c-a)} = \frac{3(a-b)(b-c)(c-a)}{3(a-b)(b-c)(c-a)} = 1

∴ The value of the

\frac{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}{3(a-b)(b-c)(c-a)}

is 1.

© examsnet.com

Go to Question:

Prev Question

Next Question