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Question

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

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Solution

Given: x=5+353 and y=535+3
Consider x=5+353

Rationallsing 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
[1.5]

Consider, y=5353
Rationalising the denominator,

y=(53)2(53)(5+3)
y=(5)2215+(3)2(5)2(3)2
y=5215+353
y=82162
y=415
[1.5]

Now, x+y+xy
=4+15+415+(4+15)(415)
=8+42(15)2
=8+1615
=9
[2]

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