Exams › JEE Main › Maths

Solve the system of equations: 1/(y - 1) - 1/(y + 1) = 1/x and y² - x - 5 = 0.

1. x = 4, y = +-3
2. x = 4, y = 3 only
3. x = -4, y = +-3
4. x = 2, y = +-3

Correct answer: x = 4, y = +-3

Solution

1/(y-1) - 1/(y+1) = [(y+1) - (y-1)]/(y² - 1) = 2/(y² - 1) = 1/x, so x = (y² - 1)/2. From the second equation x = y² - 5. Equate: (y² - 1)/2 = y² - 5 => y² - 1 = 2y² - 10 => y² = 9 => y = +-3. Then x = y² - 5 = 4. Both signs of y are valid (y = +-1 would be excluded, but +-3 are fine).

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 →