Question

$\frac{768\times 768\times 768+232\times 232\times 232}{768\times 768-768\times 232+232\times 232}=$?

• A. $1000$
• B. $536$
• C. $500$
• D. $268$
• E. None of these

Answer 1

Answer: (A)

$1000$

Let $a=768$ and $b=232$.

Then, the given expression,

$\frac{768\times 768\times 768+232\times 232\times 232}{768\times 768-768\times 232+232\times 232}$ can be written as:

$=\frac{(a^3+b^3)}{(a^2+b^2-ab)}$

[We know, $(a^3+b^3)=(a+b)(a^2+b^2-ab)$]

$=\frac{(a+b)(a^2+b^2-ab)}{(a^2+b^2-ab)}$

$=(a+b)=(768+232)=1000$.

Therefore, option $A$ is correct.