$$\frac{{{{\left( {4.53 - 3.07} \right)}^2}}}{{\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}} + \, $$     $$\frac{{{{\left( {3.07 - 2.15} \right)}^2}}}{{\left( {2.15 - 4.53} \right)\left( {4.53 - 3.07} \right)}} + \,\, $$     $$\frac{{{{\left( {2.15 - 4.53} \right)}^2}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)}}$$     is simplified to :

A. 0

B. 1

C. 2

D. 3

Answer: Option D

Solution(By Examveda Team)

Given expression :
$$ = \frac{{{{\left( {4.53 - 3.07} \right)}^3} + {{\left( {3.07 - 2.15} \right)}^3} + {{\left( {2.15 - 4.53} \right)}^3}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}}$$
Let (4.53 - 3.07) = $$a$$, (3.07 - 2.15) = $$b$$ and (2.15 - 4.53) = $$c$$
$$\eqalign{ & = \frac{{{a^3} + {b^3} + {c^3}}}{{abc}} \cr & = \frac{{3abc}}{{abc}} \cr & = 3 \cr} $$
[∵ If a + b + c = 0, a ³ + b³ + c³ = 3abc]