Question
Download Solution PDFमाना कि x > 1, y > 1, z > 1 गुणोत्तर श्रेणी (GP) में हैं। तब \(\rm \frac{1}{1+ln x}, \frac{1}{1+lny}, \frac{1}{1+\ln z}\) हैं
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है,
x, y, z गुणोत्तर श्रेढ़ी (GP) में हैं
इस प्रकार,
⇒ y2 = xz
⇒ \(2lny = lnx + lnz\)
lnx, ln y और lnz समांतर श्रेढ़ी (AP) में हैं।
⇒ (1 + lnx), (1 + lny) और (1 + lnz) समांतर श्रेढ़ी (AP) में हैं।
⇒ \(\frac{1}{1+lnx}, \frac{1}{1+lny}, \frac{1}{1+lnz}\) हरात्मक श्रेढ़ी (HP) में हैं।
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