Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
18.5k views
in Sets, relations and functions by (50.2k points)

If x and y are positive integers satisfying tan-1(1/x) + tan-1(1/y) = tan-1(1/7), then find the number of ordered pairs of (x, y)

1 Answer

+1 vote
by (54.5k points)
selected by
 
Best answer

Given equation is

tan-1(1/x) + tan-1(1/y) = tan-1(17)

tan-1(1/x) + tan-1(1/y)

7x + 7y = xy - 1

y = ((7x + 1)/(x - 7))

Hence, the possible ordered pairs are

(8, 57), (9, 32), (12, 17), (17, 12), (32, 9), (57, 8)

Thus, the number of ordered pairs is 6.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...