If x = 3 - √8 then x + 1/x = _____?
- 6
- 7
- 8
- None of these
Explanation
Given x = 3 - √8:
Step 1: Find 1/x
To rationalize the denominator, first simplify √8 to 2√2.
x = 3 - 2√2
1/x = 1 / (3 - 2√2)
Multiply numerator and denominator by the conjugate (3 + 2√2):
1/x = (3 + 2√2) / ((3 - 2√2)(3 + 2√2))
= (3 + 2√2) / (9 - 8)
= 3 + 2√2
Step 2: Calculate x + 1/x
x + 1/x = (3 - 2√2) + (3 + 2√2)
= 6
Related MCQs
- 2x² + 4 = 9x
- 2x² + 9 = 4x
- 2x² + 9 = 4x
- x² + 4 = 9x
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