రెండు తీగలు AB మరియు CD బిందువు O వద్ద కలుస్తే మరియు AO = (9x - 2) సెం.మీ., BO = (2x + 2) సెం.మీ., CO = 4x సెం.మీ. మరియు DO = (7x - 2) సెం.మీ., అప్పుడు, AO (x> 1) విలువను కనుగొనండి?

  1. 12 సెం.మీ.
  2. 14 సెం.మీ.
  3. 16 సెం.మీ.
  4. 18 సెం.మీ.

Answer (Detailed Solution Below)

Option 3 : 16 సెం.మీ.
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Detailed Solution

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మనకు తెలిసినది,

AO × OB = OC × OD

⇒ (9x – 2) × (2x + 2) = (4x) × (7x – 2)

⇒ 18x2 – 4x + 18x – 4 = 28x2 – 8x

⇒ 10x2 – 22x + 4 = 0

⇒ 10x2 – 20x – 2x + 4 = 0

⇒ 10x(x – 2) – 2(x – 2) = 0

⇒ (x – 2)(10x – 2)  = 0

⇒ x = 2 or x = 0.2

⇒ x = 2

AO = (9x – 2) = (18 – 2) = 16 సెం.మీ.

AO యొక్క విలువ 16 సెం.మీ.

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