document.write( "Question 760067: Find the sum of the squares of the three solutions of the equation x^3+(3x)^2-7x+1=0
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Algebra.Com's Answer #462459 by KMST(5328) $\"\"$ $\"About$

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$\"%283x%29%5E2=3%5E2%2Ax%5E2=9x%5E2\"$ so $\"x%5E3%2B%283x%29%5E2-7x%2B1=0\"$ means $\"x%5E3%2B9x%5E2-7x%2B1=0\"$
\n" ); document.write( "You may have meant $\"x%5E3%2B3x%5E2-7x%2B1=0\"$ , where only the $\"x\"$ is squared.
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\n" ); document.write( "THE PROBLEM AS POSTED:
\n" ); document.write( "Let the solutions of $\"x%5E3%2B%283x%29%5E2-7x%2B1=0\"$ be $\"a\"$ , $\"b\"$ , and $\"c\"$ .
\n" ); document.write( "The full factorization of the polynomial $\"x%5E3%2B%283x%29%5E2-7x%2B1\"$ must be
\n" ); document.write( " $\"x%5E3%2B%283x%29%5E2-7x%2B1=%28x-a%29%28x-b%29%28x-c%29\"$
\n" ); document.write( "If we multiply that factorization we get
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\n" ); document.write( "From that, we get
\n" ); document.write( " $\"-%28a%2Bb%2Bc%29=9\"$ --> $\"a%2Bb%2Bc=-9\"$ and
\n" ); document.write( " $\"ab%2Bac%2Bbc=-7\"$
\n" ); document.write( "If we multiply, we find that
\n" ); document.write( " $\"%28a%2Bb%2Bc%29%5E2=a%5E2%2Bb%5E2%2Bc%5E2%2B2%28ab%2Bbc%2Bac%29\"$
\n" ); document.write( "Replacing the values found for the polynomial,
\n" ); document.write( " $\"%28-9%29%5E2=a%5E2%2Bb%5E2%2Bc%5E2%2B2%28-7%29\"$ --> $\"81=a%5E2%2Bb%5E2%2Bc%5E2-14\"$ --> $\"a%5E2%2Bb%5E2%2Bc%5E2=81%2B14\"$ --> $\"a%5E2%2Bb%5E2%2Bc%5E2=95\"$
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\n" ); document.write( "IF THE PROBLEM EQUATION IS $\"x%5E3%2B3x%5E2-7x%2B1=0\"$ :
\n" ); document.write( "Let the solutions of $\"x%5E3%2B3x%5E2-7x%2B1=0\"$ be $\"a\"$ , $\"b\"$ , and $\"c\"$ .
\n" ); document.write( "The full factorization of the polynomial $\"x%5E3%2B%283x%29%5E2-7x%2B1\"$ must be
\n" ); document.write( " $\"x%5E3%2B3x%5E2-7x%2B1=%28x-a%29%28x-b%29%28x-c%29\"$
\n" ); document.write( "If we multiply that factorization we get
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\n" ); document.write( "From that, we get
\n" ); document.write( " $\"-%28a%2Bb%2Bc%29=3\"$ --> $\"a%2Bb%2Bc=-3\"$ and
\n" ); document.write( " $\"ab%2Bac%2Bbc=-7\"$
\n" ); document.write( "If we multiply, we find that
\n" ); document.write( " $\"%28a%2Bb%2Bc%29%5E2=a%5E2%2Bb%5E2%2Bc%5E2%2B2%28ab%2Bbc%2Bac%29\"$
\n" ); document.write( "Replacing the values found for the polynomial,
\n" ); document.write( " $\"%28-3%29%5E2=a%5E2%2Bb%5E2%2Bc%5E2%2B2%28-7%29\"$ --> $\"9=a%5E2%2Bb%5E2%2Bc%5E2-14\"$ --> $\"a%5E2%2Bb%5E2%2Bc%5E2=9%2B14\"$ --> $\"a%5E2%2Bb%5E2%2Bc%5E2=23\"$ \n" ); document.write( "

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