Question
Download Solution PDFIf, \(\frac{r}{13} + \frac{13}{r} = 1\) then the value of r3 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\frac{r}{13} + \frac{13}{r} = 1\)
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
Last updated on Jun 13, 2025
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