Let x = √13 + √11 and y =1 then the

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Let x = √13 + √11 and y = 1 then the value of 3x² – 5xy + 3y² is
√13 − √11 x

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 − √11		√13 + √11

=	(√13 + √11)²
	(√13)² − (√11)²

=	13 + 11 + 2√143
	13 − 11

=	24 + 2√143	= 12 + √143
	2

∴ y =	1	=	1
	x		12 + √143

=	1	×	12 − √143
	12 + √143		12 − √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

Let x =	√13 + √11	and y =	1	then the value of 3x² – 5xy + 3y² is
	√13 − √11		x