Question
Download Solution PDFयदि दो वास्तविक संख्याओं के वर्गों का योग 26 है और उनका योग 6 है, तो इन दो संख्याओं के घन का योग क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
मान लीजिए कि दो वास्तविक संख्याएँ x और y हैं।
वर्गों का योग: x2 + y2 = 26
संख्याओं का योग: x + y = 6
प्रयुक्त सूत्र:
(x + y)2 = x2 + y2 + 2xy
x3 + y3 = (x + y)(x2 + y2 - xy)
गणनाएँ:
x + y = 6
(x + y)2 = 62
x2 + y2 + 2xy = 36
26 + 2xy = 36
2xy = 36 - 26
2xy = 10
xy = 5
अब, हमें घनों का योग, x3 + y3 ज्ञात करने की आवश्यकता है:
x3 + y3 = (x + y)(x2 + y2 - xy)
x + y, x2 + y2, और xy के ज्ञात मानों को प्रतिस्थापित करें:
x3 + y3 = (6)(26 - 5)
x3 + y3 = (6)(21)
x3 + y3 = 126
इसलिए, दो संख्याओं के घनों का योग 126 है।
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