Given that a ,b ,c are distinct real num...

Given that `a ,b ,c` are distinct real numbers such that expressions `a x^2+b x+c ,b x^2+c x+aa n dc x^2+a x+b` are always non-negative. Prove that the quantity `(a^2+b^2+c^2)//(a b+b c+c a)` can never lie inn `(-oo,1)` .

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