The discussion revolves around solving the equation √(6 + 3√2) = √a + √b, with a and b expressed in the form a + b√c. Participants are examining the reasoning behind the assertion that a + b = 6 based on their attempts to manipulate the equation.
The conversation is ongoing, with participants recognizing that multiple solutions may exist. They are exploring different interpretations of the equation and considering alternative approaches to find solutions, while acknowledging the complexity of potential outcomes.
There is a focus on finding simple solutions, and participants express concern about the complexity of other potential solutions. The original problem context includes specific forms for a and b, which may influence the direction of the discussion.
BMW said:Homework Statement
Solve the equation √(6 + 3√2) = √a + √b, writing a and b in the form a + b√c.Homework Equations
In the answers they say that a + b = 6, but I cannot see how they can say this.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.
BMW said:Ah, ok. So there would be many other solutions, and they are only finding one such solution?
Dick said:Right. There are many other solutions. They are just looking for a nice simple one.
BMW said: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)?