document.write( "Question 446754: The sum of the roots of 8x² - 2x = 1 is: \n" ); document.write( "

Algebra.Com's Answer #307649 by josmiceli(19441) $\"\"$ $\"About$

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if I say the roots are $\"+r%5B1%5D+\"$ and $\"+r%5B2%5D+\"$ ,
\n" ); document.write( " $\"+x+=+r%5B1%5D+\"$
\n" ); document.write( " $\"+x+=+r%5B2%5D+\"$
\n" ); document.write( "then
\n" ); document.write( " $\"+x+-+r%5B1%5D+=+0+\"$
\n" ); document.write( " $\"+x+-+r%5B2%5D+=+0+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+%28x+-+r%5B1%5D%29%2A%28x+-+r%5B2%5D%29+=+0+\"$
\n" ); document.write( "(1) $\"+x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29x+%2B+r%5B1%5D%2Ar%5B2%5D+=+0+\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"+8x%B2+-+2x+=+1+\"$
\n" ); document.write( " $\"+8x%5E2+-+2x+-+1+=+0+\"$
\n" ); document.write( "(2) $\"+x%5E2+-+%281%2F4%29%2Ax+-+1%2F8+=+0+\"$
\n" ); document.write( "Comparing (2) with (1),
\n" ); document.write( " $\"+r%5B1%5D+%2B+r%5B2%5D+=+1%2F4+\"$
\n" ); document.write( "The sum of the roots is 1/4
\n" ); document.write( "check:
\n" ); document.write( "Complete the square:
\n" ); document.write( " $\"+x%5E2+-+%281%2F4%29%2Ax+=+1%2F8++\"$
\n" ); document.write( " $\"+x%5E2+-+%281%2F4%29%2Ax+%2B+%281%2F8%29%5E2+=+1%2F8+%2B+%281%2F8%29%5E2+\"$
\n" ); document.write( " $\"+%28+x+-+1%2F8+%29%5E2+=+8%2F64+%2B+1%2F64+\"$
\n" ); document.write( " $\"+%28+x+-+1%2F8+%29%5E2+=+9%2F64+\"$
\n" ); document.write( " $\"+x+-+1%2F8+=+3%2F8+\"$
\n" ); document.write( " $\"+x+=+1%2F2+\"$
\n" ); document.write( "and, also
\n" ); document.write( " $\"+x+-+1%2F8+=+-3%2F8+\"$
\n" ); document.write( " $\"+x+=+-1%2F4+\"$
\n" ); document.write( " $\"+r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+-+1%2F4+\"$
\n" ); document.write( " $\"+r%5B1%5D+%2B+r%5B2%5D+=+1%2F4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );