Question
Download Solution PDFयदि p + q + r = 13 और pq + qr + rp = 30 है, तो p3 + q3 + r3 − 3pqr का मान है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया :
p + q + r = 13
pq + qr+ rp = 30
प्रयुक्त सूत्र:
x3 + y3 + z3 - 3xyz = (x +y +z) [( x + y + z)2 - 3(xy + yz + zx )]
जहाँ, x, y और z चर हैं।
गणना:
यहाँ, हमारे पास p + q + r = 13 और pq + qr + rp = 30 है
अब, जैसा कि हम जानते हैं,
⇒ p3 + q3 + r3 - 3pqr = (p + q + r) [ (p + q + r)2 - 3(pq + qr + rp)]
⇒ p3 + q3 + r3 - 3pqr = 13[(13)2 - 3 × 30]
⇒ p3 + q3 + r3 - 3pqr = 13[169 - 90]
⇒ p3 + q3 + r3 - 3pqr = 13 × 79 = 1027
अतः, अभीष्ट मान 1027 है।
Last updated on Jul 11, 2025
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