MathDB

Symmetric square root equality

Source: 2014 BAMO-12 #3

February 22, 2016

algebrapolynomialsquare roots

Problem Statement

Suppose that for two real numbers

x

and

y

the following equality is true:

(x+ \sqrt{1+ x^2})(y+\sqrt{1+y^2})=1

Find (with proof) the value of

x+y

.

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