Mathematics
Assertion (A): 53 - 33 - 23 = 3 x 5 x -3 x -2
Reason (R): ∵ 5 - 3 - 2 = 0
⇒ 53 - 33 - 23 = 53 + (-3)3 + (-2)3
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
Expansions
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Answer
By property,
If a + b + c = 0, then
⇒ a3 + b3 + c3 = 3abc
Given,
⇒ 53 - 33 - 23
⇒ 53 + (-3)3 + (-2)3
Let a = 5, b = -3 and c = -2.
∴ a + b + c = 5 + (-3) + (-2) = 5 - 3 - 2 = 0
⇒ a3 + b3 + c3 = 3abc
⇒ 53 + (-3)3 + (-2)3 = 3 × 5 × (-3) × (-2)
∴ Both A and R are true, and R is the correct reason for A.
Hence, option 3 is the correct option.
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