document.write( "Question 1134096: If the expression x=sqrt(2+sqrt(2+sqrt(2+sqrt(2+...) extends to an infinite number of roots and converges to a positive number x, what is x? \n" ); document.write( "

Algebra.Com's Answer #751393 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Square both sides:\r\n" );
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document.write( "Subtract 2 from both sides:\r\n" );
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document.write( "The right side is the same as the right side of the\r\n" );
document.write( "original equation so it's just x:\r\n" );
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document.write( "x+1=0;  x-2=0\r\n" );
document.write( "  x=-1;   x=2\r\n" );
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document.write( "We discard the negative answer because the radical\r\n" );
document.write( "always means the POSITIVE square root.\r\n" );
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document.write( "Answer: x=2\r\n" );
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document.write( "Edwin

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