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Solving Equations with Variable on Both Sides

132.If x+y=20...

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132.If x+y=2013 and 1/x+1/y=2013,what is the value of xy?

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α

β

x^{2} - x + 1 = 0

, then the value of

α^{2013} + β^{2013}

Q. The number of common tangents to

y^{2} = 2012 x

x y = (2013)^{2}

α

β

are the roots of

x^{2} - x + 1 = 0

, then the value of

α^{2013} + β^{2013}

Q. If x and y are positive integers, what is the value of

\sqrt{x} + \sqrt{y}

x + y = 15

\sqrt{x y} = 6

x = 1 + a + a^{2} + . . . . \infty

y = 1 + b + b^{2} + . . . . \infty,

then the value of

1 + a b + + a^{2} b^{2} + . . . . \infty

(0 < a < 1, 0 < b < 1)

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