यदि तीन क्रमागत संख्याओं का योग 15 है तो मध्य संख्या का वर्ग क्या होगा?

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MP Police Constable 2023 Official Paper (Held On: 02 Sept, 2023 Shift 2)
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  1. 16
  2. 25
  3. 36
  4. 9

Answer (Detailed Solution Below)

Option 2 : 25
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दिया गया है:

तीन क्रमागत संख्याओं का योग = 15

प्रयुक्त सूत्र:

यदि तीन क्रमागत संख्याएँ x-1, x और x + 1 हैं, तो उनका योग है:

(x - 1) + x + (x + 1) = 15

मध्य संख्या का वर्ग = x2

गणना:

मान लीजिए कि तीन क्रमागत संख्याएँ x - 1, x और x + 1 हैं।

उनका योग है:

(x - 1) + x + (x + 1) = 15

⇒ x - 1 + x + x + 1 = 15

⇒ 3x = 15

⇒ x = 15 ÷ 3

⇒ x = 5

मध्य संख्या 5 है।

मध्य संख्या का वर्ग:

⇒ x2 = 52 = 25

मध्य संख्या का वर्ग 25 है।

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