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a and b are consecutive, positive integers such that a^2−b^2>22. What is the minimum possible value of a+b?

  • Maths -

    since a and b are consective integers we could say that
    a = b+1
    then let the difference be
    (b+1)^2 - b^2 > 22
    b^2 + 2b + 1 - b^2 > 22
    2b > 21
    b > 10.5
    so b has to be 11
    a = 12
    So a+b = 23

    check: 12^2 - 11^2 = 144-121 = 23 which is > 22
    try another value:
    13^2-12^2 = 25
    11^2-10^2 = 21

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