Question

if x=3-2√2 then find value of x^2-1/x^2

Answer 1

Hope this will help you..

Given x = 3 + 2√2
⇒ x = 2 + 1 + 2√2 × 1 v
⇒ x = (√2)2 + 12 + 2 × √2 × 1
⇒ x = (√2 + 1)2
∴ √x = (√2 + 1)
⇒ 1/√x = 1/(√2 + 1)
Multiply and divide with (√2 – 1)   
 1/√x = (√2 – 1)/[(√2 – 1)(√2 + 1)]   
         = (√2 – 1)/(2 – 1)
∴  1/√x = (√2 – 1)
Now consider, (√x + 1/√x) = (√2 + 1) + (√2 – 1)
Therefore, (√x + 1/√x) = 2√2

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