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Find the Minimum value of 9 cos 2x + 2 sec 2x1). 3√22). 2√33). 6√34). 6√2 |
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Answer» Solution: According to AM-GM inequality, Here a = 9 cos²x and b = 2 sec²x Note: AM- GM inequality can be used ANYWHERE keeping in mind that a and b are positive. So, (9 cos²x + 2 sec²x)/2≥√(9cos²x)(2sec²x) (9 cos²x + 2 sec²x)/2≥√(9/sec²x)(2sec²x) (9 cos²x + 2 sec²x)/2≥√(9)(2) (9 cos²x + 2 sec²x)/2≥√18 (9 cos²x + 2 sec²x)≥2√18 (9 cos²x + 2 sec²x)≥2×3√2 (9 cos²x + 2 sec²x)≥6√2 So, the minimum value is 6√2. The correct OPTION is 4). 6√2 |
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