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Question

If x=5+353 and y=535+3, then x+y+xy=

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Solution

Given: x=5+353, y=535+3

Consider x=5+353

Rationalising the denominator,

x=(5+3)2(53)(5+3)

x=(5)2+215+(3)2(5)2(3)2

x=5+215+353

x=8+2152

x=4+15

Consider y=535+3

Rationalising the denominator,

y=(53)2(53)(5+3)

y=(5)2215+(3)2(5)2(3)2

y=5215+353

y=82152

y=415

Now, x+y+xy

=4+15+415+(4+15)(415)

=8+42(15)2

=8+1615

=9

Hence, (a) is the correct option.

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