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Scaled reciprocal (ay +/- b/y = k): rescale, then square

This type of question, asked 7 times: 14 Jul 2023 S1, 19 Jul 2023 S2, 20 Jul 2023 S2, 20 Jul 2023 S3, 24 Jul 2023 S4, 11 Sep 2024 S3, 23 Sep 2024 S3. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jul 2023 S1

    61
    If 7b−14b=77b - \frac{1}{4b} = 7, then what is the value of 16b2+149b216b^2 + \frac{1}{49b^2}?

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  2. Question 2

    19 Jul 2023 S2

    68
    If (3y−3y)=5\left(3y - \frac{3}{y}\right) = 5, find the value of (y2+1y2)\left(y^2 + \frac{1}{y^2}\right).

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  3. Question 3

    20 Jul 2023 S2

    68
    If (5y+5y)=11\left(5y + \frac{5}{y}\right) = 11, find the value of (y2+1y2)\left(y^2 + \frac{1}{y^2}\right).

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  4. Question 4

    20 Jul 2023 S3

    73
    If (2y+2y)=7\left(2y + \frac{2}{y}\right) = 7, find the value of (y2+1y2)\left(y^2 + \frac{1}{y^2}\right).

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  5. Question 5

    24 Jul 2023 S4

    67
    If (4y−4y)=13\left(4y - \frac{4}{y}\right) = 13, find the value of (y2+1y2)\left(y^2 + \frac{1}{y^2}\right).

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  6. Question 6

    11 Sep 2024 S3

    61
    If x+19x=3x + \frac{1}{9x} = 3, then the value of 9x2+19x29x^2 + \frac{1}{9x^2} is:

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  7. Question 7

    23 Sep 2024 S3

    57
    Let 3t−13t=33t - \frac{1}{3t} = 3, then which of the following expressions has the value equal to 12?

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