document.write( "Question 1149213: Solve For Y: {sqrt{y+sqrt{y+sqrt{y+..}}}=5} \n" ); document.write( "

Algebra.Com's Answer #770565 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "You are given\r\n" );
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document.write( "     = 5.          (1)\r\n" );
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document.write( "Square both sides.  Then the very first square root sign goes away, and you get\r\n" );
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document.write( "    y +   = 25.    (2)\r\n" );
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document.write( "In the left side, the second addend is equal to 5, again (!)\r\n" );
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document.write( "So, your equation  (2)  takes the form\r\n" );
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document.write( "    y + 5 = 25.     (3).\r\n" );
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document.write( "From (3), you momentarily get\r\n" );
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document.write( "    y = 25 - 5 = 20.\r\n" );
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document.write( "ANSWER.  y = 20.\r\n" );
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document.write( "    It is not a joke.  It is the standard way to solve such problems.\r\n" );
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document.write( "    CHECK.  Consider this sequence\r\n" );
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document.write( "             = 4.472...\r\n" );
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document.write( "             = 4.947...\r\n" );
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document.write( "             = 4.995...\r\n" );
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document.write( "You see the sequence, which, OBVIOUSLY, converges, and converges to the value of 5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Yes, it is a TRICK.   Focus - pocus, which you can learn only from a Math circle or
\n" ); document.write( "from reading special books, developing Math skills for young lovers of Math.\r
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\n" ); document.write( "\n" ); document.write( "So, today it is as if you visited a Math circle . . . \r
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\n" ); document.write( "\n" ); document.write( "            Come again soon to this forum to learn something new (!)\r
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\n" ); document.write( "\n" ); document.write( "To see some other similar or close Math problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Evaluating expressions that contain infinitely many square roots\r
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