document.write( "Question 175567: x4 + 2x2 – 1 = 0 \n" ); document.write( "

Algebra.Com's Answer #130668 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E4+%2B+2x%5E2-1+=+0\"$
\n" ); document.write( "You can use a substitution and knock this down to a quadratic equation.
\n" ); document.write( "Let $\"z=x%5E2\"$
\n" ); document.write( " $\"x%5E4%2B2x%5E2-1=0\"$
\n" ); document.write( " $\"z%5E2%2B2z-1=0\"$
\n" ); document.write( "Use the quadratic formula,
\n" ); document.write( " $\"z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"z+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"z+=+%28-2+%2B-+sqrt%28+4%2B4%29%29%2F%282%29+\"$
\n" ); document.write( " $\"z+=+-1+%2B-+sqrt%282%29\"$
\n" ); document.write( "Two solutions for z.
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\n" ); document.write( "First solution for z,
\n" ); document.write( " $\"z+=+-1+%2B+sqrt%282%29\"$
\n" ); document.write( " $\"x%5E2+=+-1+%2B+sqrt%282%29\"$
\n" ); document.write( "Two real roots,
\n" ); document.write( " $\"x+=0+%2B-+sqrt%28-1+%2B+sqrt%282%29%29\"$
\n" ); document.write( "or approximately
\n" ); document.write( " $\"x=0.643\"$ and $\"x=-0.643\"$
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\n" ); document.write( "Second solution for z,
\n" ); document.write( " $\"z+=+-1+-+sqrt%282%29\"$
\n" ); document.write( " $\"x%5E2=+-1+-+sqrt%282%29\"$
\n" ); document.write( "Two complex roots,
\n" ); document.write( " $\"x%5E2=+%28-1%29%2A%281%2Bsqrt%282%29%29\"$
\n" ); document.write( " $\"x=+0+%2B-+sqrt%28%28-1%29%2A%281%2Bsqrt%282%29%29%29\"$
\n" ); document.write( " $\"x=+0+%2B-+sqrt%281%2Bsqrt%282%29%29i\"$
\n" ); document.write( "or approximately
\n" ); document.write( " $\"x=1.554i\"$ and $\"x=-1.554i\"$
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\n" ); document.write( "The graph verifies the real roots.
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\n" ); document.write( ".
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-2%2C+2%2C+-10%2C+10%2C+x%5E4%2B2x%5E2-1%29+\"$ \n" ); document.write( "

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