Question
Download Solution PDFIf (X - \(\rm \frac{1}{x}\)) = 6, and x > 0, find the value of (x2 - \(\rm \frac{1}{x^2}\)).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
x - 1/x = 6
Formula Used
x + 1/x = √ ((x - 1/x)2 + 4)
x2 - 1/x2 = (x - 1/x)(x + 1/x)
Calculation:
x - 1/x = 6
x + 1/x = √ ((x - 1/x)2 + 4)
⇒ x + 1/x = √(40)
⇒ x + 1/x = 2√10
x2 - 1/x2 = (x - 1/x)(x + 1/x)
= 2√10 × 6
= 12√10
The answer is 12√10
Last updated on Jun 13, 2025
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