Question
Download Solution PDFदो प्राकृतिक संख्याओं के बीच अंतर का घन 1728 है, जबकि इन दोनों दी गई संख्याओं का गुणनफल 108 है। इन दो संख्याओं के घनों के बीच धनात्मक अंतर ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
(पहली प्राकृतिक संख्या - दूसरी प्राकृतिक संख्या)3 = 1728
पहली प्राकृतिक संख्या × दूसरी प्राकृतिक संख्या = 108
प्रयुक्त सूत्र:
(A - B)3 = A3 - B3 - 3AB × (A - B)
गणना:
माना पहली प्राकृतिक संख्या = A
दूसरी प्राकृतिक संख्या = B
(A - B)3 = 1728
⇒ (A - B) = 3√1728 = 12
A3 - B3 = (A - B)3 + 3AB × (A - B)
⇒ 1728 + 3 × 108 × 12
⇒ 1728 + 3 × 108 × 12
⇒ 1728 + 3888 = 5616
∴ सही उत्तर 5616 है।
Last updated on Jul 19, 2025
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