document.write( "Question 1106262: pls help me to answer this problem: Simplify: \sqrt{5+\sqrt{5+\sqrt{5+\ldots}}} \n" ); document.write( "

Algebra.Com's Answer #721225 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let x = .     (1)\r\n" );
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document.write( "It is what you ask to simplify.\r\n" );
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document.write( "Square both sides of (1). You will get\r\n" );
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document.write( "x^2 = 5 + x,     or\r\n" );
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document.write( "x^2 - x - 5 = 0.\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "Since x, obviously, must be > 0, only positive root is the solution:  x = .\r\n" );
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document.write( "Answer.   = .\r\n" );
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\n" ); document.write( "Amazingly, isn't it ?\r
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\n" ); document.write( "\n" ); document.write( "Let me show you another, even more amazing calculation !\r
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\n" ); document.write( "\n" ); document.write( "Simplfy $\"sqrt%282+%2B+sqrt%282+%2B+sqrt%282+%2B+ellipsis%29%29%29\"$ .\r
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document.write( "Let x = .     (2)\r\n" );
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document.write( "It is what I want to simplify.\r\n" );
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document.write( "Square both sides of (2). You will get\r\n" );
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document.write( "x^2 = 2 + x,     or\r\n" );
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document.write( "x^2 - x - 2 = 0.\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
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document.write( " =  =  = .\r\n" );
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document.write( "Since x, obviously, must be > 0, only positive root is the solution:  x =  = 2.\r\n" );
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document.write( "Answer.   = 2.\r\n" );
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\n" ); document.write( "Next time, please, use plain text format ONLY when post problems to this forum.\r
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\n" ); document.write( "\n" ); document.write( "Other formats are UNREADABLE.\r
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\n" ); document.write( "\n" ); document.write( "It was a miracle that I was able to decipher and read it.\r
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