Question

Assertion: 18³ + (–10)³ + (–8)³ = 4320

Reason: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

Explanation:

Assertion (A) states: 18³ + (–10)³ + (–8)³ = 4320. 

Using the identity for three numbers (x, y, z) whose sum is zero:

x³ + y³ + z³ = 3xyz if x + y + z = 0 

Here, 18 + (–10) + (–8) = 0.

So, 18³ + (–10)³ + (–8)³

= 3 × 18 × (–10) × (–8)

= 4320 

Hence, Assertion (A) is true.

Reason (R) states: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx 

This is a standard algebraic identity and is true.

However, Reason (R) is an algebraic identity for the square of a sum and has no direct connection to the cubic identity used in the Assertion (A).

Therefore, while both statements are true, Reason (R) does not explain Assertion (A).