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
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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