Question
Download Solution PDF9 এবং 13 থেকে কোন ক্ষুদ্রতম ধনাত্মক সংখ্যা বিয়োগ করলে তাদের তৃতীয় সমানুপাতী 18 হবে?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
18 হল তৃতীয় সমানুপাতী।
ব্যবহৃত ধারণা:
1. যদি A : B :: C : D হয় তাহলে (B × C) = (A × D)
2. (a - b)2 = a2 - 2ab + b2
গণনা:
ধরা যাক ক্ষুদ্রতম ধনাত্মক সংখ্যাটি Q
সমানুপাতটি হবে (9 - Q) : (13 - Q) : : (13 - Q) : 18
প্রশ্নানুসারে,
(13 - Q)2 = (9 - Q) × 18
⇒ 169 + Q2 - 26Q = 162 - 18Q
⇒ Q2 - 8Q + 7 = 0
⇒ (Q - 7)(Q - 1) = 0
সুতরাং, ক্ষুদ্রতম সংখ্যা = Q = 1
∴ ক্ষুদ্রতম সংখ্যাটি হল 1.
Last updated on Jul 16, 2025
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