1.

If a2 - 2a = 1, then what is the value of \({a^3} - \frac{1}{{{a^3}}}\)?1. 142. 183. 214. 24

Answer» Correct Answer - Option 1 : 14

Given:

a2 - 2a = 1

Formula Used:

(a - b)3 = a3 - b3 - 3a2b + 3ab2 = a3 - b3 - 3(ab)(a - b)

If (a - 1/a) = p

Then, (a3 - 1/a3) = p3 + 3p

Calculation:

a2 - 2a = 1

Divide by 'a'

⇒ a - 2 = 1/a

⇒ a - 1/a = 2

Now,

if (a - 1/a) = 2

∴ Then, (a3 - 1/a3) = (2)3 + 3(2) = 14


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