If, \(\frac{r}{13} + \frac{13}{r} = 1\) then the value of r3 is:

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SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 3)
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  1. -2157
  2. 2197
  3. 2157
  4. -2197

Answer (Detailed Solution Below)

Option 4 : -2197
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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Given:

\(\frac{r}{13} + \frac{13}{r} = 1\)

Concept used:

If x + (1/x) = 1

then x3 = - 1

Calculation:

Let (r/13) = x

According to the question:

⇒ \(\frac{r}{13} + \frac{13}{r} = 1\)

⇒ x + 1/x = 1

then x3 = - 1

Now, putting the value of x

⇒ (r/13)3 = - 1

⇒ r3 = - 2197

∴ The correct answer is -2197.

Additional InformationGiven - x + 1/x = 1

Formula Used - a3 + b3 = (a + b)(a2 – ab + b2)

Calculation:

x + 1/x = 1

⇒ x2 + 1 = x

⇒ x2 - x + 1 = 0      ---(1)

Multiply (x + 1) into both side of eq (1)

⇒ (x + 1)( x2 – x + 1) = 0

⇒ x3 + 1 = 0

⇒ x3 = -1

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