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  1. If x =
    1
    , y =
    1
    , then the value of 8xy (x2 + y2) is
    2 + √32 − √3
    1. 196
    2. 290
    3. 112
    4. 194
Correct Option: C

x =
1
2 + √3

=
1
×
1
=
2 − √3
2 + √3 2 − √ 3 4 − 3

= 2 − √ 3
∴  y =
1
= 2 + √ 3
2 − √ 3

∴  x + y = 2 – √ 3 + 2 + √ 3 = 4
xy = (2 – √ 3 ) (2 + √ 3 )
= 4 – 3 = 1
∴  8xy (x2 + y2)
= 8xy [(x + y)2 – 2 xy]
= 8 × 1 (42 – 2 × 1)
= 8 (16 – 2) = 8 × 14 = 112



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