Which of the following inequalities are NOT correct?
(A) If \(a>1, b>1\), then \(\log _b a+\log _a b \leq 2\)
(B) For any real number \(x,\left(9^x+9^{1-x}\right) \geq 9\)
(C) If \(a, b, c\) are non-zero real numbers of the same sign, then \(\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right) \leq 3\)
(D) If \(a, b, c\) are three distinct real numbers, then \((a+b)(b+c)(c+a) \geq 8 a b c\)
Choose the correct answer from the options given below:

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.