Exams › JEE Main › Maths

If x = (7 + 5*sqrt(2))^(1/3) - 1/(7 + 5*sqrt(2))^(1/3), find the value of x³ + 3x - 14.

1. 1
2. 0
3. 2
4. 4

Correct answer: 0

Solution

Using the algebraic identity (a - 1/a)³ = a³ - 1/a³ - 3(a - 1/a), we get x³ + 3x = a³ - 1/a³. Since 1/(7+5sqrt(2)) = -(7-5sqrt(2)) (as the denominator 49-50 = -1), we get a³ - 1/a³ = 14. Therefore x³ + 3x - 14 = 0.

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 →