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Math Help - Value of Integers

  1. #1
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    Value of Integers

    Let u and v be two positive real numbers satisfying the two equations u+v+uv=10 and u^2 +v^2=40. What is the value of integer closest to
    u+v?
    a)4
    b)5
    c)6
    d)6
    e)8
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  2. #2
    Senior Member Dinkydoe's Avatar
    Joined
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    Observe that  40 = (u+v)^2-2uv = (u+v)^2-2(10-(u+v))
    This gives:
    60= (u+v)^2+2(u+v)

    Let x = u+v. Thus solve 60 = x^2+2x for x and determine the digit closest to x.
    Last edited by Dinkydoe; January 13th 2010 at 05:40 AM. Reason: switched +/-
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