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Suppose a , b are integers and a + b is a root of x ^2+ ax + b =0 . What is the maximum possible values of b^2 ?

Correct answer

81

Step-by-step solution

If " a+b " is a root it satisfies the equation Hence (a+b)^2+a(a+b)+b=0 2 a ^2+3 ba + ( b ^2+ b )=0 Now since " a " is an integer Discriminant is a perfect square aligned & 9 ~b ^2-8 ( ~b ^2+ b )= p ^2 for same p Z & ( ~b -4)^2-16= p ^2 & ( ~b -4+ b )( b -4- p )=16 & ~b -4+ p = 8, ~b -4- p = 2, ~b -4+ p = b -4- p = 4 aligned So, b-4=5,-5,4,-4 b =9,-1,8,0 ( ~b ^2 )_ =81

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