यदि (5 + 3√2) (5 - 3√2) का धनात्मक वर्गमूल α है, तो 8 + 2α का धनात्मक वर्गमूल क्या होगा ?

This question was previously asked in
CDS Elementary Mathematics 16 April 2023 Official Paper
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  1. 2 + √3
  2. 3 - √2
  3. √7 - 1
  4. √7 + 1

Answer (Detailed Solution Below)

Option 4 : √7 + 1
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प्रयुक्त सूत्र:

(a - b) (a + b) = a2 - b2

(a2 + 2ab + b2) = (a + b)2

गणना:

दिया गया है कि,

α  = √[(5 + 3√2) (5 - 3√2)]

चूँकि, (a - b) (a + b) = a2 - b2

α = √[(52 - (3√2)2]

α = √(25 - 18) = √7

माना अभीष्ट वर्गमूल β है

β = √(8 + 2√7) = √(7 + 1 + 2√7)

β = √[(√7)2 + 2.1.√7 +  (1)2]

β = √(√7 + 1)2 

चूँकि (a2 + 2ab + b2) = (a + b)2

β = √7 + 1

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