document.write( "Question 1205480: if a + b = -3 and b - c = 6, find the value of $\"2a%5E2+-+3b%5E2+%2B+c%5E2\"$ \r
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Algebra.Com's Answer #842322 by ikleyn(52862) $\"\"$ $\"About$

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\n" ); document.write( "if a + b = -3 and b - c = 6, find the value of $\"2a%5E2+-+3b%5E2+%2B+c%5E2\"$ .
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document.write( "if a + b = -3 and b - c = 6, then\r\n" );
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document.write( "   a = -3 - b    (1)\r\n" );
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document.write( "and\r\n" );
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document.write( "   c = b - 6     (2)\r\n" );
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document.write( "Substitute these expressions  (1)  and  (2)  into  .\r\n" );
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document.write( "You will get then\r\n" );
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document.write( "      2a^2 - 3b^2 + c^2 = 2*(-3-b)^2 - 3b^2 + (b-6)^2 = 2*(9 + 6b + b^2) - 3b^2 + b^2 - 12b + 36 = \r\n" );
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document.write( "    = 18 + 12b + 2b^2 - 3b^2 + b^2 - 12b + 36 = 54 + (12b-12b) + (3b^2-3b^2) = 54.    \r\n" );
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document.write( "ANSWER.  Under the given constrains,   = 54.\r\n" );
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