document.write( "Question 145269This question is from textbook basic technical Mathematics
\n" ); document.write( ": exercises 14.1 question 14\r
\n" ); document.write( "\n" ); document.write( "y=2x^2-1
\n" ); document.write( "x^2+2y^2=16 \n" ); document.write( "

Algebra.Com's Answer #105958 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "First I'll approach it graphically to see what\r\n" );
document.write( "to expect; then I'll do it algebraically\r\n" );
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document.write( "The graph of  is this parabola:\r\n" );
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document.write( "The graph of  is this ellipse:\r\n" );
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document.write( "Put them together on one graph:\r\n" );
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document.write( "The graph of  is this ellipse:\r\n" );
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document.write( "Since these graphs cross in two points, these will be two\r\n" );
document.write( "real solutions, and since parabolas and circles could cross\r\n" );
document.write( "as many as 4 times, there will two imaginary solutions as well\r\n" );
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document.write( "The first equation is already solved for , so we substitute\r\n" );
document.write( " for  in the second equation:\r\n" );
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document.write( "That does not factor, so we solve that for \r\n" );
document.write( "using the quadratic formula:\r\n" );
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document.write( "where , , \r\n" );
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document.write( "So we have two solutions for \r\n" );
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document.write( " and \r\n" );
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document.write( "If we substitute the first value of  in , we get\r\n" );
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document.write( "  \r\n" );
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document.write( "If we substitute the second value of  in , we get\r\n" );
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document.write( "The first value of  gives these two solutions for x:\r\n" );
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document.write( " and \r\n" );
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document.write( "The second value of gives these two solutions for x:\r\n" );
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document.write( ", ,\r\n" );
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document.write( "but since  is a negative number, it's going to be\r\n" );
document.write( "imaginary, so we factor  out of it, ,\r\n" );
document.write( "so we have\r\n" );
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document.write( "and of course \r\n" );
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document.write( "So we have four solutions for (,)\r\n" );
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document.write( "(, ) = (, ) \r\n" );
document.write( "(, ) = (, ) \r\n" );
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document.write( "These are the points where the curves above cross, and are the two\r\n" );
document.write( "real solutions.\r\n" );
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document.write( "Here are the two imaginary solutions:\r\n" );
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document.write( "(, ) \r\n" );
document.write( "(, )\r\n" );
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document.write( "Edwin

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