Exams › JEE Advanced › Maths
Given that x + 1/x = 2, prove that x² + 1/x² = x⁴ + 1/x⁴ = x⁸ + 1/x⁸. The common value of all three expressions is:
- 2
- 0
- 4
- 1
Correct answer: 2
Solution
The equation x + 1/x = 2 has the unique real solution x = 1 (since the AM-GM minimum of x + 1/x for x > 0 is 2, attained at x = 1). With x = 1, every power xⁿ = 1, so xⁿ + 1/xⁿ = 2 for all n. Hence all three expressions equal 2.
Related JEE Advanced Maths questions
- In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
- Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
- Identify the periodic function among the following:
- The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
- Let f(x) = 4x / (4x² + 2). If the sum of the integrals ∫(1/1997) + ∫(2/1997) +... + ∫(1196/1997) equals 499q, what is the value of q?
- Given that α, β, γ, and θ are the smallest positive angles in increasing order for which their sine values equal a positive constant k, what is the result of 4 sin(α/2) + 3 sin(β/2) + 2 sin(γ/2) + sin(θ/2)?
⚔️ Practice JEE Advanced Maths free + battle 1v1 →