Verified answer

1/x + 1/y = 1

x + y = 4

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(x + y)/xy = 1

x + y = 4

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4 = xy

x + y = 4

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x = 4 - y

4 = (4 - y)y

y^2 - 4y + 4 = 0

(y - 2)^2 = 0

x = 2

y = 2