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# Help pls

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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