document.write( "Question 729484: The sum of the squares of the solution x^2+2kx-5=0 is 26. Find the value of k.\r
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Algebra.Com's Answer #445896 by MathLover1(20855) $\"\"$ $\"About$

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given:\r
\n" ); document.write( "\n" ); document.write( "The sum of the squares of the solution $\"x%5E2%2B2kx-5=0\"$ is $\"26\"$ . \r
\n" ); document.write( "\n" ); document.write( "Find: the value of $\"k\"$ \r
\n" ); document.write( "\n" ); document.write( "first find the solution $\"x%5E2%2B2kx-5=0\"$ using quadratic formula\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2kx-5=0\"$ .....note that coefficient $\"a=1\"$ , $\"b=2k\"$ and $\"c=-5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ ...plug in coefficients\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-%282k%29+%2B-+sqrt%28+%282k%29%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-2k+%2B-+sqrt%28+4k%5E2%2B20+%29%29%2F2+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-2k+%2B-+sqrt%28+4%28k%5E2%2B5%29+%29%29%2F2+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-2k+%2B-+2sqrt%28+%28k%5E2%2B5%29+%29%29%2F2+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-cross%282%29k+%2B-+cross%282%29sqrt%28+%28k%5E2%2B5%29+%29%29%2Fcross%282%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-k+%2B-+sqrt%28+%28k%5E2%2B5%29+%29%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions involving $\"k\"$ :\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-k+%2B+sqrt%28k%5E2%2B5%29+\"$ or $\"x+=+-k+-+sqrt%28k%5E2%2B5%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "since given the sum of the squares of the solution is $\"26\"$ , we have\r
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\n" ); document.write( "\n" ); document.write( " $\"+%28-k+%2B+sqrt%28k%5E2%2B5%29%29%5E2%2B%28-k+-sqrt%28k%5E2%2B5+%29%29%5E2=26\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+k%5E2+%2B+k%5E2%2B5%2Bk%5E2+%2Bk%5E2%2B5=26\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+4k%5E2+%2B10=26\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+4k%5E2+=26-10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+4k%5E2+=16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+k%5E2+=16%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+k%5E2+=4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+k+=sqrt%284%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+k+=2\"$ or $\"+k+=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2kx-5=0\"$ ...plug in value for $\"k\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"+k+=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2%2A2x-5=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B4x-5=0\"$ ........find solutions\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-4+%2B-+sqrt%28+16%2B20+%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-4+%2B-+sqrt%28+36+%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-4+%2B-+6%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-4+%2B+6%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+2%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=1+\"$ \r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-4+-+6%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-10%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=-5+\"$ \r
\n" ); document.write( "\n" ); document.write( "if we do second solution above we will get $\"x+=-1+\"$ and $\"x+=5+\"$ \r
\n" ); document.write( "\n" ); document.write( "so, solutions of the $\"x%5E2%2B2kx-5=0\"$ are:\r
\n" ); document.write( "\n" ); document.write( " $\"x+=1+\"$ and $\"x+=-5+\"$
\n" ); document.write( "or
\n" ); document.write( " $\"x+=-1+\"$ and $\"x+=5+\"$ \r
\n" ); document.write( "\n" ); document.write( "now check if the sum of the squares of the solution $\"x%5E2%2B2kx-5=0\"$ is $\"26\"$ :\r
\n" ); document.write( "\n" ); document.write( " $\"1%5E2%2B%28-5%29%5E2=26+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1%2B25=26+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"26=26+\"$ ......true\r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"%28-1%29%5E2%2B5%5E2=26+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1%2B25=26+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"26=26+\"$ ......true\r
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