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math

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The sum of two numbers is 10.The sum of their squares is 52.Find the numbers.

  • math - ,

    one number --- x
    the other ---- 10-x
    x^2 + (10-x)^2 = 52
    x^2 + 100 - 20x + x^2 = 52
    2x^2 - 20x + 48 = 0
    x^2 - 10x + 24 = 0
    (x-6)(x-4) = 0
    x = 6 or x=4

    if one is 6, the other is 4
    if one is 4 the other is 6
    (symmetrical answers)

    the two numbers are 6 and 4

    check: 6+4 = 10
    36+16 = 52
    all is good!

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