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Value of sqrt(1 + root3/2) - sqrt(1 - root3/2) and expressions in it

This type of question, asked 2 times: 29 Jan 2022 Tier II, 3 Feb 2022 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    29 Jan 2022 Tier II

    83
    If x=1+32−1−32x = \sqrt{1 + \frac{\sqrt{3}}{2}} - \sqrt{1 - \frac{\sqrt{3}}{2}}, then the value of 3−x3+x\frac{\sqrt{3} - x}{\sqrt{3} + x} (corrected to two decimal places) is:

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  2. Question 2

    3 Feb 2022 Tier II

    59
    If 1+32−1−32=c\sqrt{1 + \frac{\sqrt{3}}{2}} - \sqrt{1 - \frac{\sqrt{3}}{2}} = c, then the value of c is:

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