Question
Download Solution PDF\(\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}\) के विस्तार में कितने पद हैं, जहाँ a ≠ 0, b ≠ 0 है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
यदि a और b वास्तविक संख्याएँ हैं और n एक धनात्मक पूर्णांक है, तो
\(\rm 0 \leq r \leq n\) के लिये (a + b)n = nC0 an + nC1 an - 1 b1 + ......... nCn bn
(a + b)n = n + 1 में पदों की कुल संख्या
गणना:
हमें \(\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}\) में पदों की कुल संख्या ज्ञात करनी है जहां a ≠ 0, b ≠ 0
⇒\([{\rm \left(\frac{a}{b}+\frac{b}{a}\right)^{2}}]^{21}\)
⇒\({\rm \left(\frac{a}{b}+\frac{b}{a}\right)^{42}}\)
∴ व्यंजक में पदों की कुल संख्या 42 + 1 = 43 है।
Last updated on May 30, 2025
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