Question

If $x^a\times x^b\times x^c=1$ then $a^3+b^3+c^3$ is equal to:

• A. 9
• B. abc
• C. a + b + c
• D. 3abc

Answer 1

The correct option is D 3abc

$x^a\times x^b\times x^c=1$
$\Rightarrow x^{a+b+c}=1=x^0$
$\Rightarrow a+b+c=0$
Now since $a^3+b^3+c^3-3abc$
$=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)$
$\Rightarrow a^3+b^3+c^3-3abc=0$
$\therefore a^3+b^3+c^3=3abc$
Hence , (d) is the right choice.