Question

x = √7 +√2 / √7 -√2

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Answer 1

Answer:

Given, x = √7 +√2 / √7 -√2

= (√7 +√2 / √7 -√2)(√7 +√2/√7 +√2)

= (√7 +√2)²/[ (√7)² - (√2)² ]

=> x = (7 + 2 + 2×√7×√2)/ 7-2

x = ( 9 + 2√14 ) / 5

Answer 2

$\frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} - \sqrt{2} } ( \sqrt{7 } + \sqrt{2)} = \frac{7 + \sqrt{14} + \sqrt{14} + 2}{7 + \sqrt{14} - \sqrt{14} - 2}$

$\frac{9 + \sqrt{14} + \sqrt{14} }{5 + \sqrt{14} - \sqrt{14} } = \frac{9 + \sqrt{14} + \sqrt{14} }{5}$

$\frac{9 + 2 \sqrt{14} }{5}$