document.write( "Question 1187915: the roots of 2x^2 +3x-1=0 are alpha and beta. Find the values of [alpha square +1÷beta square] [beta square+1÷alpha square]\r
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Algebra.Com's Answer #818929 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "the roots of 2x^2 +3x-1=0 are alpha and beta.
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document.write( "To make my writing easier, I will use  \"a\" instead of alpha  and \"b\" instead of bete.\r\n" );
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document.write( "So, I need find  \"%28a%5E2+%2B+1%2Fb%5E2%29%2A%28b%5E2+%2B+1%2Fa%5E2%29\".\r\n" );
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document.write( "We have\r\n" );
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document.write( "    \"%28a%5E2+%2B+1%2Fb%5E2%29%2A%28b%5E2+%2B+1%2Fa%5E2%29\" = \"a%5E2%2Ab%5E2\" + 1 + 1 + \"1%2F%28a%5E2%2Ab%5E2%29\".\r\n" );
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document.write( "According to Vieta's theorem,  \"a%2Ab\" = \"-1%2F2\".  THEREFORE,  \"a%5E2%2Ab%5E2\" = \"%28-1%2F2%29%5E2\" = \"1%2F4\".\r\n" );
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document.write( "HENCE,  \r\n" );
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document.write( "    \"%28a%5E2+%2B+1%2Fb%5E2%29%2A%28b%5E2+%2B+1%2Fa%5E2%29\" = \"a%5E2%2Ab%5E2\" + 1 + 1 + \"1%2F%28a%5E2%2Ab%5E2%29\" = \"1%2F4+\"+ 2 + 4 = 6 \"1%2F4\" = 6.25.    ANSWER\r\n" );
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