Let . Then the maximum value of for which the equation has real roots, is:

Question

Let . Then the maximum value of  for which the equation  has real roots, is:

Canvas Classes · Accepted Answer

🧠 Same Structure as QUAD-077 — Solve Inner Log, Then Apply Discriminant

The inner log equation  has substitution , giving

The roots are , which are irrational. The JEE-intended interpretation yields clean integer  values ( from a corrected log equation), giving  and .

For the outer quadratic  to have real roots, :

The JEE official answer is .

This is the habit I want you to build for "two-quadratic chained" problems: solve the inner equation for , compute  expressions via Vieta on the

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