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  1. If x = ³√2 + √3 , then the value of x3 +
    1
    		  is
    x3

    1. 8
    2. 9
    3. 2
    4. 4
Correct Option: D

x = ³√2 + √3
Cubing on both sides ,
⇒ x3 = 2 + √3

1
 =
1
x3 2 + √3

1
 =
1 × ( 2 - √3 )
x3( 2 + √3 ) × ( 2 - √3 )

=
2 - √3
= 2 - √3
4 - 3

∴ x3 +
1
 = 2 + √3 + 2 - √3 = 4
x3


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