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If x = 3 + 2√2, find the value of \({\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)^2}\)

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If x = 3 + 2√2, find the value of \({\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)^2}\)
1). 2√2
2). 4√2
3). 2
4). 4


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1 answers

1 vote
Answered by on | Votes 1 |

x = 3 + 2√2

$({\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)^2})$ 

= x + 1/x – 2

= (3 + 2√2) + 1/(3 + 2√2) – 2

= (3 + 2√2) + (3 - 2√2)/[(3 + 2√2) (3 - 2√2)] – 2

= 3 + 2√2 + 3 - 2√2 – 2

= 4

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