x − \(\rm\frac{1}{x}\) = 3 అయితే, x3\(\rm\frac{1}{x^3}\) విలువ కనుగొనండి?

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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. ఇవి ఏవి కావు

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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ఇచ్చినది:

x - 1/x = 3

ఉపయోగించిన భావన:

a3 - b3 = (a - b)3 + 3ab(a - b)

గణన:

గుర్తింపును వర్తింపజేయడం:

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

⇒ x3 - (1/x)3 = (3)3 + 3(1)(3)

⇒ x3 - (1/x)3 = 27 + 9

⇒ x3 - (1/x)3 = 36

∴ x3 - (1/x)3 యొక్క విలువ 36.

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