If a b c = 0 then find the value of ( a^2/ bc b^2 / ca c^2 ab )?

Question

If a  b c = 0 then find the value of ( a^2/ bc   b^2 / ca   c^2   ab )?

Answer

Solution:

Given, abc = 0

Let's consider two cases here:

Case 1: One of the values of a, b, or c is equal to 0

If a=0, then (a^2/bc) is equal to 0, b^2/ca is equal to 0, c^2/ab is equal to 0, and ab is equal to 0, thus the value of (a^2/bc + b^2/ca + c^2/ab) is also equal to 0.

If b=0, then (a^2/bc) is undefined, b^2/ca is equal to 0, c^2/ab is equal to 0, and ab is equal to 0, thus the value of (a^2/bc + b^2/ca + c^2/ab) is also undefined.

If c=0, then (a^2/bc) is equal to 0, b^2/ca is undefined, c^2/ab is equal to 0, and ab is equal to 0, thus the value of (a^2/bc + b^2/ca + c^2/ab) is also undefined.

Case 2: Two or more values of a, b, or c are equal to 0

If two values of a, b, or c are equal to 0, then the value of (a^2/bc + b^2/ca + c^2/ab) is undefined.

If all three values of a, b, and c are equal to 0, then the value of (a^2/bc + b^2/ca + c^2/ab) is also equal to 0.

Therefore, the value of (a^2/bc + b^2/ca + c^2/ab) is either 0 or undefined, depending on the values of a, b, and c.

Answer

Answer

A + b + c = 0

=> a3 + b3 + c3 = 3abc

a3/abc+ b

3/abc + c3/abc

= 3
or
a2/bc+ b

2/ac + c2/ab

= 3 is the solution.