Question
Download Solution PDFयदि x और y का समांतर और ज्यामितीय माध्य क्रमशः 8 और 3√7 है, तो x3 + y3 का मान क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
समांतर माध्य (A.M) = 8
ज्यामितीय माध्य (G.M) =3√7
प्रयुक्त सूत्र:
A.M = (a + b)/2
G.M = √ (ab)
x3 + y3 = ( x + y )3 - 3xy(x + y)
गणना:
प्रश्न के अनुसार,
⇒ A.M = (x + y)/2
⇒ 8 = (x + y)/2
⇒ x + y = 16
⇒ G.M = √(xy)
⇒ 3√7 = √(xy)
दोनों पक्षों का वर्ग करने पर, हमें प्राप्त होता है
⇒ 9 × 7 = xy
⇒ xy = 63
अब,
⇒ x3 + y3 = (x + y)3 - 3xy(x + y) = (16)3 - 3 × 63 × 16 = 4096 - 3024 = 1072
अतः x3 + y3 का मान 1072 है।
Last updated on Jul 15, 2025
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