Question
Download Solution PDFयदि X तथा \(\rm \frac{1}{x}(x\ne0)\) का औसत M हो, तो x2 और \(\rm \frac{1}{x^2}\) का औसत कितना होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
x और 1/x का औसत = M
प्रयुक्त सूत्र:
औसत = संख्याओं का योग / संख्याओं की संख्या
(a + b)2 = a2 + b2 + 2ab
गणना:
दिया गया है कि x और 1/x का औसत M है।
(x + 1/x) / 2 = M
⇒ x + 1/x = 2M
⇒ (x + 1/x)2 = (2M)2
⇒ x2 + 2(x)(1/x) + 1/x2 = 4M2
⇒ x2 + 2 + 1/x2 = 4M2
⇒ x2 + 1/x2 = 4M2 - 2
अब, x2 और 1/x2 का औसत निम्नानुसार है:
(x2 + 1/x2) / 2
औसत = (4M2 - 2) / 2
औसत = 2M2 - 1
∴ x2 और 1/x2 का अभीष्ट औसत 2M2 - 1 है।
Last updated on May 14, 2025
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