If x − \(\rm\frac{1}{x}\) = 3, the value of x3 − \(\rm\frac{1}{x^3}\) is

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Bihar STET Paper I: Mathematics (Held In 2019 - Shift 1)
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  1. 36
  2. 63
  3. 99
  4. none of these

Answer (Detailed Solution Below)

Option 1 : 36
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Bihar STET Paper 1 Mathematics Full Test 1
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Detailed Solution

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Given:

x - 1/x = 3

Concept used:

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

Calculation:

x3 - 1/x3 = (x - 1/x)3 + 3 × x × 1/x × (x - 1/x)

⇒ (x - 1/x)3 + 3(x - 1/x)

⇒ (3)3 + 3 × (3)

⇒ 27 + 9 = 36

∴ The value of x3 - 1/x3 is 36.

Alternate Method If x - 1/x = a, then x3 - 1/x3 = a3 + 3a

Here a = 3

x - 1/x3 = 33 + 3 × 3

= 27 + 9

= 36

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