document.write( "Question 1118033: If sqrt(5)= 2+ 1/a, show that a= 4+1/a \n" ); document.write( "

Algebra.Com's Answer #733260 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "If sqrt(5)= 2+ 1/a, show that a= 4+1/a
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document.write( "If  = 2 + ,  then   =      (1)\r\n" );
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document.write( "It implies   a =     (2)\r\n" );
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document.write( "Rationalize the denominator in the right side of (2):\r\n" );
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document.write( "a =  = . =  =  = .   (3)\r\n" );
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document.write( "Now in the formula  a = 4 +     (*)\r\n" );
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document.write( "    the left  side is  a =     (according to (3))\r\n" );
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document.write( "    the right side is  4 +  =  (now replace  by , based on (1), to get )  = 4 +  = .\r\n" );
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document.write( "Thus the both sides of (*) are the same.\r\n" );
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document.write( "The statement is proved.\r\n" );
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