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We know \(a=\sqrt{11}+\sqrt{13},b=\sqrt{11}+2\sqrt{13}\) and \(c=\sqrt{11}+3\sqrt{13}\) The expression \(a^2(b-c)+b^2(c-a)+c^2(a-b)\)evaluates to a number which can be written in the form \(p\sqrt{q}\) for integers p and q, where q is square-free. Find p+q.

 Oct 29, 2022
 #1
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The expression evaluates to 4*sqrt(143), so the answer is 147.

 Oct 29, 2022
 #2
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a^2(b-c)+b^2(c-a)+c^2(a-b) = - 26sqrt(13)

 

p  +  q = - 26 + 13 = - 13

 Oct 29, 2022

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