express (2+sqrt3)(5-2sqrt3) in the form a+bsqrtc.

the answer is 4+sqrt3.

can someone teach me how to get it ?

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- Jun 3rd 2006, 09:28 PM #1

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- Jun 3rd 2006, 10:00 PM #2

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Originally Posted by**charl0tte**

$\displaystyle

(2+\sqrt 3)(5-2\sqrt 3)=2(5-2\sqrt 3)+\sqrt 3 (5-2\sqrt 3)

$$\displaystyle

=10-4\sqrt 3 + \sqrt 3 (5-2\sqrt 3)

$

$\displaystyle

=10-4\sqrt 3 + 5\sqrt 3-2\sqrt 3 \sqrt 3

$

$\displaystyle

=10-4\sqrt 3 + 5\sqrt 3-6

$

$\displaystyle

=4+\sqrt 3

$

RonL

- Jun 4th 2006, 03:42 AM #3