document.write( "Question 519668: how do you solve the following:\r
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Algebra.Com's Answer #345745 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The other tutor's solution is incorrect\r\n" );
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document.write( " +  = \r\n" );
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document.write( "Since one of the radicals is isolated, we square both sides:\r\n" );
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document.write( "To make things a little easier, \r\n" );
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document.write( "let A = \r\n" );
document.write( "let B = \r\n" );
document.write( "let C = \r\n" );
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document.write( "Then the above equation becomes:\r\n" );
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document.write( "         A + B = C\r\n" );
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document.write( "Squaring both sides:\r\n" );
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document.write( "      (A + B)² = C²\r\n" );
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document.write( "(A + B)(A + B) = C²\r\n" );
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document.write( " A² + 2AB + B² = C² \r\n" );
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document.write( "Since A = , then A² = x+4\r\n" );
document.write( "Since B = , then B² = 2x-1\r\n" );
document.write( "let C = , then C² = 7x+1\r\n" );
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document.write( "So now we have\r\n" );
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document.write( " x+4 + 2AB + 2x-1 = 7x+1\r\n" );
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document.write( "Simplify and solve for 2AB\r\n" );
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document.write( " 3x + 3 + 2AB = 7x + 1\r\n" );
document.write( "          2AB = 4x - 2\r\n" );
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document.write( "Divide through by 2 since all coefficients are even:\r\n" );
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document.write( "           AB = 2x - 1\r\n" );
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document.write( "Square both sides again:\r\n" );
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document.write( "        (AB)² = (2x - 1)²\r\n" );
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document.write( "         A²B² = (2x - 1)(2x - 1)              \r\n" );
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document.write( "         A²B² = 4x² - 4x + 1\r\n" );
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document.write( "Now substitute A² = x+4  and B² = 2x-1 from above:\r\n" );
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document.write( " (x+4)(2x-1) = 4x² - 4x + 1 \r\n" );
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document.write( " 2x² + 7x - 4 = 4x² - 4x + 1\r\n" );
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document.write( " -2x² + 11x - 5 = 0\r\n" );
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document.write( "  2x² - 11x + 5 = 0\r\n" );
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document.write( "(x - 5)(2x - 1) = 0\r\n" );
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document.write( "x - 5 = 0;  2x - 1 = 0\r\n" );
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document.write( "    x = 5;      2x = 1\r\n" );
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document.write( "                 x = \r\n" );
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document.write( "Check each solution as they may be extraneous: \r\n" );
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document.write( "Checking x = 5\r\n" );
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document.write( " +  = \r\n" );
document.write( " +  = \r\n" );
document.write( " +  = \r\n" );
document.write( "3 + 3 = 6\r\n" );
document.write( "    6 = 6\r\n" );
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document.write( "That checks so x = 5 is a solution.\r\n" );
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document.write( "Checking x = \r\n" );
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document.write( " +  = \r\n" );
document.write( " +  = \r\n" );
document.write( " +  = \r\n" );
document.write( " +  = \r\n" );
document.write( " + 0 = \r\n" );
document.write( " = \r\n" );
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document.write( "That checks also, so x =  is also a solution.\r\n" );
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document.write( "Edwin

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