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Rationalise surd fractions into a + b root k, then find an expression in a and b

This type of question, asked 2 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    60
    If 14−8+3+223−22−3−223+22=a+b2\frac{1}{4 - \sqrt{8}} + \frac{3 + 2\sqrt{2}}{3 - 2\sqrt{2}} - \frac{3 - 2\sqrt{2}}{3 + 2\sqrt{2}} = a + b\sqrt{2}, then what is the value of (3a+4b)(3a + 4b)?

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  2. Question 2

    29 Jan 2022 Tier II

    96
    If 22242−3+5=a+5b\frac{22\sqrt{2}}{4\sqrt{2} - \sqrt{3 + \sqrt{5}}} = a + \sqrt{5}b, with a,b>0a, b > 0, then what is the value of (ab):(a+b)(ab) : (a + b)?

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