document.write( "Question 252245: What is the sum of the squares of the roots of x^4 - 5 x^2 + 6 = 0 \n" ); document.write( "

Algebra.Com's Answer #184070 by josmiceli(19441) $\"\"$ $\"About$

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solving the equation:
\n" ); document.write( " $\"x%5E4+-+5+x%5E2+%2B+6+=+0\"$
\n" ); document.write( "Let $\"z+=+x%5E2\"$
\n" ); document.write( " $\"+z%5E2+-+5z+%2B+6+=+0+\"$
\n" ); document.write( " $\"z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( " $\"b+=+-5\"$
\n" ); document.write( " $\"c+=+6\"$
\n" ); document.write( " $\"z+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"z+=+%285+%2B-+sqrt%2825+-+24+%29%29%2F2+\"$
\n" ); document.write( " $\"z+=+%285+%2B+1%29%2F2\"$
\n" ); document.write( " $\"z+=+3\"$
\n" ); document.write( "and
\n" ); document.write( " $\"z+=+%285+-+1%29%2F2\"$
\n" ); document.write( " $\"z+=+2\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "Substituting:
\n" ); document.write( " $\"x%5E2+=+3\"$
\n" ); document.write( " $\"x+=+sqrt%283%29\"$
\n" ); document.write( " $\"x+=+-sqrt%283%29\"$
\n" ); document.write( " $\"x%5E2+=+2\"$
\n" ); document.write( " $\"x+=+sqrt%282%29\"$
\n" ); document.write( " $\"x+=+-sqrt%282%29\"$
\n" ); document.write( "The sum of the squares of the roots is:
\n" ); document.write( " $\"3+%2B+3+%2B+2+%2B+2+=+10\"$
\n" ); document.write( " \r
\n" ); document.write( "
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