Exams › JEE Main › Maths

Let x1 and x2 be the values of x satisfying the equation [log₂(x - 2)]² + log₂(x - 2) * log₂(3/x) - 2 * [log₂(3/x)]² = 0. Which of the following is/are correct?

1. x1 + x2 = 9
2. x1 * x2 = 18
3. |x1 - x2| = 3
4. x1² + x2² = 45

Correct answer: x1 + x2 = 9

Solution

Setting a = log₂(x-2) and b = log₂(3/x), the equation factors as (a + 2b)(a - b) = 0. Solving each case with domain restrictions x > 2 and x < 3 gives two valid solutions whose sum is 9.

Related JEE Main Maths questions

• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?
• Let X and Y be two non-empty sets, and let A be a non-empty set such that X ∩ A = Y ∩ A = A and X ∪ A = Y ∪ A. Which of the following must be true?
• If A and B are non-empty sets with A containing B, then which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →