Question
Download Solution PDFयदि a > 0 और b > 0 और a + b = 1 हो तो
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
- मान लीजिए x1, x2, ..., xn ∈ R तब,
- x1, x2, ..., xn का समांतर माध्य
द्वारा परिभाषित किया गया है - x1, x2, ..., xn का ज्यामितीय माध्य
द्वारा परिभाषित किया गया है। - x1, x2, ..., xnका हरात्मक माध्य
द्वारा परिभाषित किया गया है।
- समांतर -ज्यामितीय माध्य असमानता:
≤
गणना:
दिया गया है, a > 0 और b > 0 और a + b = 1,
⇒
⇒
⇒
अब, a2 + b2 = (a + b)2 - 2ab
⇒
अब विचार करें,
∴
अत: सही उत्तर विकल्प 3 ) है
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