document.write( "Question 1051725: find the range of values of k for which kx+y=3 meets x²+y²=5 in two distinct points \n" ); document.write( "

Algebra.Com's Answer #667227 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "find the range of values of k for which kx+y=3 meets x²+y²=5 in two distinct points
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document.write( "kx + y = 3     (1)\r\n" );
document.write( "x² + y² = 5    (2)\r\n" );
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document.write( "Express y = 3-kx  from (1) and substitute it into (2). You will get\r\n" );
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document.write( " = 5.\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( " = 5,\r\n" );
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document.write( " = 0,\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Discriminant \r\n" );
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document.write( "d =  =  =  =  = .\r\n" );
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document.write( "The condition for  \"kx+y=3 meets x²+y²=5 in two distinct points\"  is  this inequality  d > 0,  or\r\n" );
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document.write( " > 0,   or, which is the same (cancel the factor 4)\r\n" );
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document.write( " > 0,  or\r\n" );
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document.write( "|k| >  = .\r\n" );
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document.write( "Answer.  kx+y=3 meets x²+y²=5 in two distinct points  if  and only if k <   OR  k > .\r\n" );
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