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  1. Let   x =
    13 + √11
    and y =
    1
    then the value of 3x2 – 5xy + 3y2 is
    13 − √11x
    1. 1717
    2. 1177
    3. 1771
    4. 1171
Correct Option: A

x =
13 + √11
13 − √11

On rationalising the denominator,
=
13 + √11
×
13 + √11
13 − √1113 + √11

=
(√13 + √11)2
(√13)2 − (√11)2

=
13 + 11 + 2√143
13 − 11

=
24 + 2√143
= 12 + √143
2

∴  y =
1
=
1
x12 + √143

=
1
×
12 − √143
12 + √14312 − √143

=
12 − √143
= 12 − √143
144 − 143

∴  x – y = 12 + √143 – 12 + √143 = 2√143
and
xy = (12 + √143)(12 – √143)
= 144 – 143 = 1
∴  3x2 – 5xy + 3y2 = 3x2 – 6xy + 3y2 + xy
= 3 (x – y)2 + xy
= 3 (2√143)2 + 1
= 3 × 4 × 143 + 1 = 1716 + 1
= 1717



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