JEE Main 2024 Mathematics question
If three successive terms of a G.P. with common ratio r (r > 1) are the lengths of the sides of a triangle and [r] denotes the greatest integer less than or equal to r, then 3[r] + [−r] is equal to .
Answer: 1
Solution
The triangle inequality gives r² − r − 1 < 0, so 1 < r < (1 + √5)/2; hence [r] = 1, [−r] = −2 and 3 − 2 = 1.