Question
Download Solution PDFयदि (a + b)2 = 36 और ab = 8 है, तब (a – b)2 का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
(a + b)2 = 36 और ab = 8
सूत्र:
(a + b)2 - (a – b)2 = 4ab
गणना:
(a + b)2 - (a – b)2 = 4ab
⇒ 36 – (a – b)2 = 4ab
⇒ (a – b)2 = 36 – 32
⇒ (a – b)2 = 4
विधि 2
(a + b)2 = 36
⇒ a2 + b2 + 2ab = 36
⇒ a2 + b2 + 2 × 8 = 36
⇒ a2 + b2 = 20 ---- (1)
अब, (a - b)2 = a2 + b2 - 2ab = 20 - 2 × 8 = 20 - 16 = 4
स्मार्ट ट्रिक
a = 4 और b = 2 लेने पर [चूँकि (a + b)2 = (4 + 2)2 = 62 = 36 और ab = 4 × 2 = 8]
(a – b)2 = (4 – 2)2 = 22 = 4
∴ सही उत्तर 4 है।
Last updated on Jun 30, 2025
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