Question
Download Solution PDFరెండు సంఖ్యల మొత్తం 17 అయితే వాటి వర్గాల మొత్తం 157. ఆ రెండు సంఖ్యల ఘనాల మొత్తాన్ని కనుగొనండి.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇచ్చిన సమస్య:
రెండు సంఖ్యల మొత్తం 17
వాటి వర్గాల మొత్తం 157
ఉపయోగించిన భావన:
x3 + y3 = (x + y)(x2 + y2 - xy)
(x + y)2 = x2 + y2 + 2xy
సాధన:
రెండు సంఖ్యలు x మరియు y గా ఉండనివ్వండి
కాబట్టి,
(x + y) = 17 మరియు (x2 + y2) = 157
ఇప్పుడు,
(x + y)2 = 289
⇒ x2 + y2 + 2xy = 289
⇒ 157 + 2xy = 289
⇒ 2xy = 289 - 157
⇒ 2xy = 132
⇒ xy = 66
ఇప్పుడు,
x3 + y3 = (x + y)(x2 + y2 - xy)
⇒ x3 + y3 = 17(157 - 66)
⇒ x3 + y3 = 17 × 91
⇒ x3 + y3 = 1547
∴ ఆ రెండు సంఖ్యల ఘనాల మొత్తం 1547.
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