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Sep 25, 2013

# If x=3-2âˆš2 , find the value of âˆšx+1/âˆšx

 If x=3-2âˆš2 , find the value of âˆšx+1/âˆšx.

Kishore Kumar

Given x = 3 â€“ 2âˆš2 â‡’ x = 2 + 1 â€“ 2âˆš2 â‡’ x = (âˆš2)2 + 12 â€“ 2 Ã— âˆš2 Ã— 1 â‡’ x = (âˆš2 â€“ 1 )2 âˆ´ âˆšx = (âˆš2 â€“ 1 ) Now consider, (1/âˆšx) = 1/(âˆš2 â€“ 1 ) Multiply and divide with (âˆš2 + 1 ), we get (1/âˆšx) = (âˆš2 + 1 )/[(âˆš2 â€“ 1 )(âˆš2 + 1 )]           = (âˆš2 + 1 )/[2 â€“ 1] âˆ´  (1/âˆšx) = (âˆš2 + 1 ) âˆšx + (1/âˆšx) = (âˆš2 â€“ 1) + (âˆš2 + 1) = 2âˆš2
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