JEE Main 2024 Mathematics question
Let the range of the function , x ∈ ℝ be [a, b]. If α and β are respectively the A.M. and the G.M. of a and b, then α/β is equal to :
Answer: (A)
Solution
sin 3x + cos 3x ranges over [−√2, √2], so f ranges over [1/(2 + √2), 1/(2 − √2)]. Then α/β = (a + b)/(2√(ab)) = ½(√(a/b)
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