यदि x = 2 -  है, तो x3 - 6x2 + 18x का मान ज्ञात कीजिए।

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SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 4)
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  1. 40
  2. 33
  3. 45
  4. 22

Answer (Detailed Solution Below)

Option 4 : 22
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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दिया गया है:

x = 2 -  + 

प्रयुक्त सूत्र:

(a - b)3 = a3 - b3 - 3ab (a - b)

गणना:

⇒ x = 2 -  + 

⇒ x - 2 =  -  -------- (1)

दोनों पक्षों का घन करने पर,

⇒ (x - 2)3 = ( - )3 

⇒ x3 - 8 - 3 × 2 × x (x - 2) = 22 - 2 - 3 ×  ×  ( - )

​​⇒ x - 8 - 6x2 + 12x = 2 - 6 ×( x - 2) [समीकरण (1) से]

​​⇒ x - 8 - 6x2 + 12x = 2 - 6x  + 12

​​⇒ x3 - 6x2 + 18x = 14 + 8 = 22

∴ सही उत्तर 22 है।

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