1.

If a(a + 3) = 4, find the value of the expression (a6 + 63a3 – 60)/4?1. 12. 03. 44. 2

Answer» Correct Answer - Option 1 : 1

Given:

a(a + 3) = 4

⇒ a2 + 3a = 4

Concept:

Cube both side of the given equation and then proceed.

Formula used:

(a + b)3 = a3 + b3 + 3ab(a + b)

Calculation:

∵ a2 + 3a = 4

On cubing both sides, we get;

(a2 + 3a)3 = 43

⇒ a6 + 27a3 + 3 × a2 × 3a(a2 + 3a) = 64

⇒ a6 + 27a3 + 3 × a2 × 3a(4) = 64

⇒ a6 + 27a3 + 36a3 = 64

⇒ a6 + 63a3 = 64      -----(1)

Putting the value of (1) in (a6 + 63a3 – 60)/4;

⇒ (64 – 60)/4

⇒ 4/4 = 1


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