document.write( "Question 1172151: 1.If r and s are the roots of the quadratic equation x2 + 3x - 5 = 0, find the value of r3 + s3. Show clear solution pls thanksss! \n" ); document.write( "
Algebra.Com's Answer #797068 by ikleyn(52805)\"\" \"About 
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document.write( "According to Vieta's theorem, we have\r\n" );
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document.write( "   r + s = -3,  rs = -5.    (1)\r\n" );
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document.write( "Keeping it in mind, we can write\r\n" );
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document.write( "    \"%28-3%29%5E3\" = \"%28r%2Bs%29%5E3\" = \"r%5E3+%2B+3r%5E2s+%2B+3rs%5E2+%2B+s%5E3\" = \"r%5E3+%2B+3rs%2A%28r%2Bs%29+%2B+s%5E3\".\r\n" );
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document.write( "Replace here  rs  by  -5  and replace  r+s  by  -3, based on (1).  You will get \r\n" );
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document.write( "   -27 = \"r%5E3+%2B+s%5E3\" + 3*(-5)*(-3) = \"r%5E3+%2B+s%5E3\" + 45,\r\n" );
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document.write( "and then\r\n" );
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document.write( "    \"r%5E3+%2B+s%5E3\" = -27 - 45 = -72.\r\n" );
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document.write( "ANSWER.   \"r%5E3+%2B+s%5E3\" = -72.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate expressions involving  \"%28x+%2B+1%2Fx%29\",  \"%28x%5E2%2B1%2Fx%5E2%29\"  and  \"%28x%5E3%2B1%2Fx%5E3%29\"\r
\n" ); document.write( "\n" ); document.write( "    - Advanced lesson on evaluating expressions\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate functions of roots of a square equation\r
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\n" ); document.write( "\n" ); document.write( "You will find there many similar problems solved.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Evaluation, substitution\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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