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June 26th, 2012, 09:06 AM   #1
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Surds

I've shown part of my solution, as it gets pretty convoluted after what I've shown. I can't tell if I'm on the right track with this one. Can anyone help me out?

Many thanks.

Q. Given that & that a & b are positive integers, find the value of a & b.

Attempt: => => => =>

Ans.: (From text book): a = 2, b = 5
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June 26th, 2012, 09:24 AM   #2
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Re: Surds

Usual method would be, starting from your original equation, multiply out the brackets.

Then for the two sides to be equal, the coefficients of root(3) on either side must be equal; and the two terms not involving root(3) must also be equal. This will give you two equations, which you can then go on to solve.
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June 26th, 2012, 10:03 AM   #3
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Re: Surds

(a + ?(3))(b - ?(3)) = ab - a?(3) + b?(3) - 3 = 7 + 3?(3).
Rational part: ab - 3 = 7
Irrational part: b - a = 3.
b = a + 3
a(a + 3) - 3 = 7
a + 3a - 10 = 0
(a - 2)(a + 5) = 0, a = 2, -5.

(a, b) = (2, 5), (-5, -2).
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June 26th, 2012, 11:01 AM   #4
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Re: Surds

Ok. Thanks guys.
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