JEE Quadratic#9

Algebra Level 4

(x2+x+2)2(a3)(x2+x+2)(x2+x+1)+(a4)(x2+x+1)2=0(x^{2}+x+2)^{2}- (a-3)(x^{2}+x+2)(x^{2}+x+1)+(a-4)(x^{2}+x+1)^{2}=0

Find the maximum integral value of aa for which the expression has at least one real root (for xx).

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