Question
Download Solution PDFযদি (a + b) 2 = 36 এবং ab = 8 হয় তবে (a - b) 2 এর মান নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত :
(a + b) 2 = 36 এবং ab = 8
সূত্র:
(a + b) 2 - (a - b) 2 = 4ab
গণনা:
(a + b)2 - (a – b)2 = 4ab
⇒ 36 – (a – b)2 = 4ab
⇒ (a – b)2 = 36 – 32
⇒ (a – b)2 = 4.
পদ্ধতি 2
(a + b)2 = 36
⇒ a2 + b2 + 2ab = 36
⇒ a2 + b2 + 2 × 8 = 36
⇒ a2 + b2 = 20 ---- (1)
এখন, (a - b)2 = a2 + b2 - 2ab = 20 - 2 × 8 = 20 - 16 = 4.
স্মার্ট ট্রিক
নেওয়া হয়েছে a = 4 এবং b = 2 [ যেহেতু (a + b)2 = (4 + 2)2 = 62 = 36 এবং ab = 4 × 2 = 8]
∴ (a – b)2 = (4 – 2)2 = 22 = 4.
Last updated on Jul 5, 2025
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