Question
Download Solution PDFకింది సమితిలోని సంఖ్యల మాదిరిగానే సంఖ్యలకు సంబంధించిన సమితిను ఎంచుకోండి?
(గమనిక: సంఖ్యలను దాని అంకెలుగా విభజించకుండా, మొత్తం సంఖ్యలపై కార్యకలాపాలు చేయాలి.)
(3, 14, 1)
(4, 36, 2)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFతర్కం : (1వ సంఖ్య యొక్క ఘనమూలం + 3వ సంఖ్య యొక్క ఘనమూలం) / 2 = 2వ సంఖ్య
ఇచ్చినది :
-
(3, 14, 1)
⇒ \({(3)^3 + (1)^3 \over 2}\) = 14
⇒ \({27 + 1 \over 2}\) = 14
⇒ \({28 \over 2}\) = 14
⇒14 = 14 (LHS = RHS)
- (4, 36, 2 )
⇒ \({(4)^3 + (2)^3 \over 2}\) = 36
⇒ \({64 + 8 \over 2}\) = 36
⇒ \({72 \over 2}\) = 36
⇒36 = 36 (LHS = RHS)
కాబట్టి,
- ఎంపిక - (1) : (8, 12, 2 )
⇒ \({(8)^3 + (2)^3 \over 2}\) = 12
⇒ \({512 + 8 \over 2}\) = 12
⇒ \({520 \over 2}\) = 12
⇒260 ≠ 12 (LHS ≠ RHS)
- ఎంపిక - (2) : (5, 81, 4)
⇒ \({(5)^3 + (4)^3 \over 2}\) = 81
⇒ \({125 + 64 \over 2}\) = 81
⇒ \({189 \over 2}\) = 81
⇒94.5 ≠ 81 (LHS ≠ RHS)
- ఎంపిక - (3) : (7, 40, 3)
⇒ \({(7)^3 + (3)^3 \over 2}\) = 40
⇒ \({343 + 27 \over 2}\) = 40
⇒ \({370 \over 2}\) = 40
⇒185 ≠ 40 (LHS ≠ RHS)
- ఎంపిక - (4) : (8, 260, 2)
⇒ \({(8)^3 + (2)^3 \over 2}\) = 260
⇒ \({512 + 8 \over 2}\) = 260
⇒ \({520 \over 2}\) = 260
⇒260 = 260 (LHS = RHS)
కాబట్టి, "ఎంపిక - (4)" సరైన సమాధానం.
Last updated on Jun 13, 2025
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