দুটি সংখ্যার যোগফল 17 এবং তাদের বর্গের যোগফল 157 হলে, এই দুটি সংখ্যার ঘন-এর যোগফল নির্ণয় করুন।

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RRB NTPC CBT 2 (Level-5) Official Paper (Held On: 12 June 2022 Shift 1)
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  1. 3791
  2. 3094
  3. 1491
  4. 1547

Answer (Detailed Solution Below)

Option 4 : 1547
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RRB NTPC CBT-I Official Paper (Held On: 4 Jan 2021 Shift 1)
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Detailed Solution

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প্রদত্ত:

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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