Exams › JEE Advanced › Maths

Solve the simultaneous equations: (x + y)/(x - y) + (x - y)/(x + y) = 13/6 and x*y = 5.

1. (x, y) = (5, 1) or (1, 5) or (-5, -1) or (-1, -5)
2. (x, y) = (5, 1) or (1, 5) only
3. (x, y) = (2.5, 2) or (2, 2.5)
4. No real solution

Correct answer: (x, y) = (5, 1) or (1, 5) or (-5, -1) or (-1, -5)

Solution

Setting t = (x+y)/(x-y) turns equation one into a solvable quadratic. Each value of t gives a linear ratio between x and y, which with xy = 5 yields the pairs.

Related JEE Advanced Maths questions

• Solve for real x: |x² + 3x + 2| + x + 1 = 0.
• Solve the equation x⁴ - 2x³ + 3x² - 2x + 1 = 0.
• 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?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →