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From two of a + b, a - b, a^2 + b^2, ab: find another (or a ratio)

This type of question, asked 6 times: 21 Jul 2023 S1, 21 Jul 2023 S3, 10 Sep 2024 S3, 19 Sep 2024 S3, 23 Sep 2024 S3, 25 Sep 2024 S3. All 6 questions below, oldest first.

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  1. Question 1

    21 Jul 2023 S1

    54
    If x+y=7x + y = 7 and xy=19xy = 19, then calculate the value of x2+y2x^2 + y^2 .

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  2. Question 2

    21 Jul 2023 S3

    60
    If x and y are positive numbers such that x - y = 5 and xy = 150, then the value of (x + y) is:

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  3. Question 3

    10 Sep 2024 S3

    68
    If x2+y2=280x^2 + y^2 = 280 and xy=120xy = 120, then find the value of x−yx+y\frac{x - y}{x + y}.

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  4. Question 4

    19 Sep 2024 S3

    75
    In a rectangular field, the sum of the length and the breadth is 9 cm and area is 18 cm218\ \text{cm}^2. If the length is 'a' and breadth is 'b', then find the value of (a2−ab+b2)(a^2 - ab + b^2).

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  5. Question 5

    23 Sep 2024 S3

    69
    If 3x+2y=103x + 2y = 10 and 2xy=72xy = 7, then find the value of 3x−2y3x - 2y (if 3x−2y>03x - 2y > 0).

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  6. Question 6

    25 Sep 2024 S3

    56
    If a2+b2=148a^2 + b^2 = 148 and ab=54ab = 54, then find the value of a+ba−b\frac{a + b}{a - b}.

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