Question
Download Solution PDFIf x = 5 - 2√6, then what is the value of √x +(1/√x)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven: x = 5 - 2√6
⇒ x = (√3 - √2)2
To find: √x +(1/√x) = √(√3 - √2)2 + 1/(√3 - √2)2
⇒ (√3 - √2) + 1/(√3 - √2)
⇒ (6 - 2√6)/(√3 - √2)
Multiplying both numerator and denominator by (√3 + √2)
⇒ (6 - 2√6) (√3 + √2)/(3 - 2)
⇒ 6√3 + 6√2 - 2√18 - 2√12
⇒ 6√3 + 6√2 - 6√2 - 4√3
⇒ 2√3
∴ the correct option is 3)Last updated on Jul 21, 2025
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