Difference between revisions of "2024 AMC 12B Problems/Problem 16"

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-==Solution 1==
--10<= a, b <= 10 , a,b has 21 choices
-per Vieta, x1x2x3  = -6, x1 + x2+ x3 = -a , x1x2+ x2x3 + x3x1 = b
-Case:
-(1)  (x1,x2,x3) = (-1,-1,6) , b = 13 not valid
-(2)  (x1,x2,x3) = (-1,1,6) , b = -1, a=-6  valid
-(3)  (x1,x2,x3) = ( 1,2,-3) , b = -7, a=0  valid
-(4)  (x1,x2,x3) = (1,-2,3) , b = -7, a=2  valid
-(5)  (x1,x2,x3) = (-1,2,3) , b = 1, a=4  valid
-(6)  (x1,x2,x3) = (-1,-2,-3) , b = 11 invalid
-so answer 4
-~[https://artofproblemsolving.com/wiki/index.php/User:Cyantist luckuso]

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