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    Question

    data-sheets-value="{"1":2,"2":"If y = 5 + 2√6, then the value of √y - (1/√y)"}" data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}">If x = 10 + 2√21, then the value of √x - (1/√x)?
    A 2√6 Correct Answer Incorrect Answer
    B 2√7 Correct Answer Incorrect Answer
    C 5√7 Correct Answer Incorrect Answer
    D 7√6 Correct Answer Incorrect Answer

    Solution

    x = 10 + 2√21 = 3 + 7 + 2√3 x √7 = √3 x √3 + √7 x √7 + 2√3 x √7 = (√3+√7)2 So x = (√3 + √7)2 So √x = (√3 + √7) Putting √x = (√3 + √7) in √x - (1/√x) we get, √x - (1/√x) = (√3 + √7) - (1/(√3 + √7) = (√3 + √7) - ((√3 - √7)) = 2√7 ` `

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