यदि m और n दो धनात्मक वास्तविक संख्याएँ इस प्रकार है कि 9m2 + n2 = 40 और mn = 4 है, तो 3m + n का मान क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 1)
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  1. 160
  2. 64
  3. 10 
  4. 8

Answer (Detailed Solution Below)

Option 4 : 8
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दिया गया:

9m² + n² = 40

mn = 4

गणना:

9m² + n² = 40

दोनों पक्षों में 6mn जोड़ने पर, हम प्राप्त करते हैं:

9m² + n² + 6mn = 40 + 6mn

⇒(3m)² + n² + 2(3m)n = 40 + 6(4)

⇒(3m + n)² = 64

⇒ 3m + n = √64 = 8

इसलिए, अभीष्ट मान 8 है।

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