Question
Download Solution PDFतीन संख्याएँ x ≤ y ≤ z जो एक-दूसरे के सह-अभाज्य हैं, इस प्रकार हैं कि पहली दो संख्याओं का गुणनफल 143 है और अंतिम दो संख्याओं का गुणनफल 195 है। तीनों संख्याओं का योग ______ है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
प्रथम दो संख्याओं का गुणनफल = 143
अंतिम दो संख्याओं का गुणनफल = 195
प्रयुक्त अवधारणा:
संख्याएँ, सह-अभाज्य होती हैं जब उनका एकमात्र उभयनिष्ठ गुणनखंड 1 होता है।
महत्तम समापवर्तक = 1
गणना:
माना संख्याएँ a, b, और c हैं
⇒ x × y = 143, y × z = 195
इन दोनों गुणनफलों में y उभयनिष्ठ है।
143 और 195 का महत्तम समापवर्तक = y = 13
⇒ a = 143/13 = 11
⇒ b = 195/13 = 15
∴ तीन सह-अभाज्य संख्याएँ 11, 13 और 15 हैं।
योग = 11 + 13 + 15 = 39
उत्तर 39 है।
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