Question
Download Solution PDFদুটি সংখ্যার যোগফল 17 এবং তাদের বর্গের যোগফল 157 হলে, এই দুটি সংখ্যার ঘন-এর যোগফল নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
দুটি সংখ্যার যোগফল = 17
তাদের বর্গের যোগফল = 157
অনুসৃত ধারণা:
x3 + y3 = (x + y)(x2 + y2 - xy)
(x + y)2 = x2 + y2 + 2xy
গণনা:
ধরি, সংখ্যা দুটি হল x এবং y
অতএব,
(x + y) = 17 এবং (x2 + y2) = 157
সুতরাং,
(x + y)2 = 289
⇒ x2 + y2 + 2xy = 289
⇒ 157 + 2xy = 289
⇒ 2xy = 289 - 157
⇒ 2xy = 132
⇒ xy = 66
অতএব,
x3 + y3 = (x + y)(x2 + y2 - xy)
⇒ x3 + y3 = 17(157 - 66)
⇒ x3 + y3 = 17 × 91
⇒ x3 + y3 = 1547
∴ এই দুটি সংখ্যার ঘন-এর যোগফল হল 1547
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