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If (x + y) = 6, what is the value of {(x – 4)3 + (y – 2)3}?
1. 1
2. 3
3. 0
4. 5

1 Answer

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Correct Answer - Option 3 : 0

Given:

(x + y) = 6

Concept:

⇒ a3 + b3 = (a + b)3 – 3ab × (a + b)

Calculation:

According to the question,

⇒ x + y = 6    …… (1)

⇒{(x – 4)3 + (y – 2)3}

⇒ (x – 4 + y – 2)3 – 3 × (x – 4) × (y – 2) × (x – 4 + y – 2)

⇒ (x + y – 6)3– 3 × (x – 4) × (y – 2) × (x + y – 6)

⇒ (6 – 6)3– 3 × (x – 4) × (y – 2) × (6 – 6)    …… {from (1)}

⇒ 0 – 3 × (x – 4) × (y – 2) × 0

⇒ 0

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