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Question:

fairydrink
fairydrink
Student
High School - 10th Grade

a+b=5 and a*b=2. Calculate the sum (a/b)+(b/a).

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Posted by fairydrink on Monday April 6, 2009 at 8:12 AM and tagged with math, product, sum.

Answers:

  1. giorgiana1976
    giorgiana1976 Teacher
    Doctorate

    eNotes Editor

    (a/b)+(b/a)=a*(a/b)+b*(b/a)=(a^2 +b^2)/a*b

    We've noticed that if we'll do a simple trick at numerator, by adding and subtracting the same quantity, meaning 2*a*b, and grouping the terms in a convenient way, we'll have:

    (a^2+2*a*b +b^2-2*a*b)/a*b=(a+b)^2/a*b - 2=21/2

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    Posted by giorgiana1976 on Monday April 6, 2009 at 8:20 AM