यदि है, तो निम्नलिखित में से कौन-सा सही है?

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NDA (Held On: 23 April 2017) Maths Previous Year paper
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  1.  एकल का एक घनमूल है
  2. x एकल का एक घनमूल है
  3. y एकल का एक घनमूल है
  4.  , -1 का एक घनमूल है

Answer (Detailed Solution Below)

Option 4 :  , -1 का एक घनमूल है
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Detailed Solution

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संकल्पना:

यदि  है, तो A की सारणिक निम्न दी गयी है:

|A| = a11 × {(a22 × a33) – (a23 × a32)} - a12 × {(a21 × a33) – (a23 × a31)} + a13 × {(a21 × a32) – (a22 × a31)}

गणना:

दिया गया है:

R1 के साथ विस्तृत करने पर, हमें निम्न प्राप्त होता है 

⇒ x (x2 – 0) – y (0 – y2) + 0 = 0

⇒ x3 + y3 = 0

अतः x/y, -1 का एक घनमूल है। 

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