Question: Simplify $ \frac{ \begin{aligned} & 24\times 24\times 24+32\times 32\times 32+45\times 45 \\ & \times 45-3\times 24\times 32\times 45 \\ \end{aligned}}{ \begin{aligned} & 24\times 24\times 32\times 32+45\times 45-24\times 32 \\ & -32\times 45-45\times 24 \\ \end{aligned}} $
Options:
A) 105
B) 101
C) 103
D) 107
Show Answer
Answer:
Correct Answer: B
Solution:
- Given expression is of the form
$ a^{3}+b^{3}+c^{3}-3abc $
$ =(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca) $
$ \therefore $ $ \frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}-ab-bc-ca}=a+b+c $
$ \therefore $ $ a+b+c=24+32+45=101 $