Question

Assertion: The value of (25)³ + (−16)³ + (−9)³ is 10800.
Reason: If a + b + c = 0, then a³ + b³ + c³ = 3abc.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(a) Both Assertion and Reason are true, and Reason is a correct explanation of Assertion.

Assertion:
Let:
$a=25,b=-16\mathrm{and}c=-9$
Now,
$a+b+c=25+\left(-16\right)+\left(-9\right)$
= 0
$$\begin{gathered} \because a+b+c=0 \\ \therefore a^3+b^3+c^3=3abc \end{gathered}$$

Thus, we have:
$3abc=\left[3\times 25\times \left(-16\right)\times \left(-9\right)\right]$
= 10800
Hence, Assertion is true.
Reason: If a + b + c = 0, then a³ + b³ + c³ = 3abc.
The given statement is true.
Therefore, both Assertion and Reason are true and Reason is a correct explanation of Assertion.