`((a-b)^(2))/((b-c)(c-a))+((b-c)^(2))/((a-b)(c-a))+`
`((c-a)^(2))/((a-b)(b-c))` का मान क्‍या है?

Options

A. 0
B. 3
C. `1/3`
D. `2`

Answer

B

Explanation

`((a-b)^(2))/((b-c)(c-a))+((b-c)^(2))/((a-b)(c-a))+`
`((c-a)^(2))/((a-b)(b-c))`
Now
`implies((a-b)^(2))/((b-c)(c-a))xx((a-b))/(a-b)`
Multiply divide by `(a-b)` in Ist term
`implies(b-c)` in IInd term
`implies(c-a)` in IIIrd term
`implies((a-b)^(2)(a-b))/((b-c)(c-a)(a-b))+`
`((b-c)^(2)(b-c))/((a-b)(b-c)(c-a))+`
`((c-a)^(2)(c-a))/((a-b)(b-c)(c-a))`
`implies` Let `a-b=x`
`b-c=y`
`c-a=z`
`:. x+y+z=0`
`:. x^(3)+y^(3)+z^(3)=3xyz`
`:. (a-b)^(3)+(b-c)^(3)+(c-a)^(3)`
`=3(a-b)(b-c)(c-a)`
`:. (3(a-b)(b-c)(c-a))/((a-b)(b-c)(c-a))=3`