Mathematics

Question

The difference between two integers is 6. The sum of their sqaures is a minimum. Find the 2 integers.
Answer with explanation gets brainliest.​

1 Answer

  • Answer:

    • 3 and - 3

    Step-by-step explanation:

    Let the numbers are x and y.

    Their difference is:

    • x - y = 6

    Sum of their squares:

    • S = x² + y²

    Substitute y = x - 6 into sum equation:

    • S = x² + (x - 6)² =
    •      x² + x² - 12x + 36 =
    •      2x² - 12x + 36

    We observe this is a quadratic expression. It has minimum value at vertex, which is when x = -b/2a or:

    • x = - (-12/2*2) = 3

    Then the value of y is:

    • y = x - 6 = 3 - 6 = - 3

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