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Solving √(6 + 3√2) = √a + √b

  1. Nov 11, 2013 #1

    BMW

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    1. The problem statement, all variables and given/known data
    Solve the equation √(6 + 3√2) = √a + √b, writing a and b in the form a + b√c.


    2. Relevant equations
    In the answers they say that a + b = 6, but I cannot see how they can say this.


    3. The attempt at a solution
    I square both sides, and that is as far as I get:
    6 + 3√2 = a + 2√(ab) + b

    In the answers, they say from here that a + b = 6. I am clueless as to how they can say this.
     
    Last edited: Nov 11, 2013
  2. jcsd
  3. Nov 11, 2013 #2

    Dick

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    I don't think they are deducing that from the equation. They are just saying 'let's look for a solution where a+b=6 and 3√2=2√(ab)'. If you can find simple numbers a and b that satisfy that then you've got a simpler form for the radical expression.
     
    Last edited: Nov 11, 2013
  4. Nov 11, 2013 #3

    BMW

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    Ah, ok. So there would be many other solutions, and they are only finding one such solution?
     
  5. Nov 11, 2013 #4

    Dick

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    Right. There are many other solutions. They are just looking for a nice simple one.
     
  6. Nov 11, 2013 #5

    BMW

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    So you would also be able to say that a + 2√(ab) = 6 and b = 3√2, and solve that way (with the risk of it being horribly complicated)?
     
  7. Nov 11, 2013 #6

    Dick

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    Yes, there are lots of ugly solutions.
     
    Last edited: Nov 11, 2013
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