Discussion

Assertion (A) : An LTI discrete system represented by the difference equation \(y(n+2) - 5y(n+1) + 6y(n) = x(n)\) is unstable.

Reason (R) : A system is unstable if the roots of the characteristic equation lie outside the unit circle.

Answer: A

Both statements are true and the reason explains the assertion, so the answer is option (A).

The characteristic equation of the system is:

\[ z^{2} - 5z + 6 = 0 \]

\[ (z - 2)(z - 3) = 0 \]

so the roots are 2 and 3. Both lie outside the unit circle, so the system is unstable, which is exactly the criterion in the reason.

Option (B) is wrong because the criterion in the reason is what settles the assertion. Options (C) and (D) call a true statement false.

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