Question
Download Solution PDF(a + b - c) = 20 மற்றும் a2+ b2 + c2 = 152 எனில், a3 + b3 - c3 + 3abc இன் மதிப்பைக் கண்டறியவும்.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFகொடுக்கப்பட்டது:
(a + b - c) = 20;
a2+ b2 + c2 = 152.
பயன்படுத்தப்படும் சூத்திரம்:
a3 + b3 = (a + b)3 - 3ab × (a + b).
கணக்கீடு:
இந்த சமன்பாட்டில் 3 மாறிகள் உள்ளன மற்றும் 2 சமன்பாடுகள் கொடுக்கப்பட்டுள்ளன.
பிறகு c = 0 என்று வைத்துக் கொள்வோம்,
⇒ (a + b) = 20
⇒ a2 + b2 = 152
இப்போது,
(a + b) = 20
இருபுறமும் வர்க்கப்படுத்தினால்,
⇒ a2 + b2 + 2ab = 400.
⇒ 152 + 2ab = 400.
⇒ 2ab = 400 - 152 = 248.
⇒ ab = 248/2 = 124.
a3 + b3 = (a + b)3 - 3ab × (a + b).
⇒ (20)3 - 3 × 124 × 20
⇒ 8000 - 7440 = 560
∴ சரியான பதில் 560.
Last updated on Jun 13, 2025
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