Question 963813
{{{x*sqrt(1+y^2)+y*sqrt(1+x^2)=0}}}
{{{x*sqrt(1+y^2)=-y*sqrt(1+x^2)}}}
{{{x^2(1+y^2)=y^2(1+x^2)}}}
{{{x^2+x^2y^2=y^2+y^2x^2}}}
{{{x^2=y^2}}}
Two solutions:
{{{y=x}}} and {{{y=-x}}}
Verify,
{{{y=x}}}
{{{x*sqrt(1+x^2)+x*sqrt(1+x^2)=0}}}
False, so this is not a solution.
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{{{y=-x}}}
{{{x*sqrt(1+x^2)-x*sqrt(1+x^2)=0}}}
{{{0=0}}}
True.
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{{{highlight(y=-x)}}}