Question

x=(3-2√2) show that (√x-1upon√x)=+-2
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Answer 1

Step-by-step explanation:

Given-----> x = ( 3 - 2√2 )

To show----> ( √x - 1 / √x ) = ± 2

Solution------> ATQ,

x = ( 3 - 2√2 )

1 / x = 1 / ( 3 - 2√2 )

Multiplying by conjugate of denominator in numerator and denominator which is ( 3 + 2√2 ) .

1 / x = ( 3 + 2√2 ) / ( 3 - 2√2 ) ( 3 + 2√2 )

= ( 3 + 2√2 ) / ( 3 )² - ( 2√2 )²

= ( 3 + 2√2 ) / ( 9 - 8 )

= ( 3 + 2√2 ) / 1 p

=> 1 / x = ( 3 + 2√2 )

Now,

x + 1 / x = ( 3 - 2√2 ) + ( 3 + 2√2 )

= 6

We know that,

( a - b )² = a² + b² - 2ab , putting a = √x , b = 1 / √x , we get,

( √x - 1 / √x )² = ( √x )² + ( 1 /√x )² - 2 ( √x ) ( 1 / √x )

= ( x + 1 / x ) - 2

=> ( √x - 1 /√x )² = 6 - 2

=> (√x - 1/√x )² = 4

=> ( √x - 1/√x ) = ± 2