Correct Answer - Option 3 : -1
Given:
The expression is
\(\frac{3^3~+~2^3~-~5^3}{9~\times~2~\times~5}\)
Formula used:
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
If a + b +c = 0 then a3 + b3 + c3 = 3abc
Calculation:
We have to find the value of
\(\frac{3^3~+~2^3~-~5^3}{9~\times~2~\times~5}\)
⇒ \(\frac{(3)^3~+~(2)^3~+~(-5)^3}{3~\times~3~\times~2~\times~5}\)
Here, 3 + 2 + (-5) = 0 so,
⇒ \(\frac{3~\times~3~\times~2~\times~(-5)}{9~\times~2~\times~5}\)
⇒ -1
∴ The value of the expression \(\frac{3^3~+~2^3~-~5^3}{9~\times~2~\times~5}\) is -1.
