document.write( "Question 906528: Hi, would you help me solve this problem, please? \r
\n" ); document.write( "\n" ); document.write( "Directions: Solve the equation by making the appropriate substitution. (meaning \"u\" for \"x\").\r
\n" ); document.write( "\n" ); document.write( "\"+x%5E%287%2F2%29-6x%5E%287%2F4%29%2B9=0+\"\r
\n" ); document.write( "\n" ); document.write( "I let \"+u=x+\" and \"+u%5E2=x%5E%287%2F2%29+\", but am unsure of how to take it from there.
\n" ); document.write( "**All of the numerators of the exponents are 7, just in case that got cut off in the formula plotting system. \r
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Algebra.Com's Answer #549925 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There is a way to make the plotting system handle fraction exponents,\r\n" );
document.write( "Place the expression in a 2x1 matrix with the blank character \"\" as the\r\n" );
document.write( "upper element and the fraction exponent as the lower element.\r\n" );
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document.write( "Don't let u=x. Let \"matrix%282%2C1%2C%22%22%2Cu=x%5E%287%2F4%29%29\" and \"matrix%282%2C1%2C%22%22%2Cu%5E2=x%5E%287%2F2%29%29+\". You had that right. \r\n" );
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document.write( "\"+matrix%282%2C1%2C%22%22%2Cx%5E%287%2F2%29-6x%5E%287%2F4%29%2B9=0%29+\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"u%5E2-6u%2B9=0\"\r\n" );
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document.write( "Then factor:\r\n" );
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document.write( "\"%28u-3%29%28u-3%29=0\"\r\n" );
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document.write( "And there's just one solution, u=3\r\n" );
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document.write( "Then \"matrix%282%2C1%2C%22%22%2Cu=x%5E%287%2F4%29%29\" becomes\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3=x%5E%287%2F4%29%29\"\r\n" );
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document.write( "Then we raise both sides to the 'reciprocal'th power, \r\n" );
document.write( "the \"4%2F7\"ths power\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3%5E%284%2F7%29=%28x%5E%287%2F4%29%29%5E%284%2F7%29%29\"\r\n" );
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document.write( "When you multiply those exponents on the right you get\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3%5E%284%2F7%29=x%5E1%29\"  \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3%5E%284%2F7%29=x%29\"\r\n" );
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document.write( "The answer is 'the seventh root of three to the fourth power'.\r\n" );
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document.write( "\"root%287%2C3%5E4%29\"\"%22%22=%22%22\"\"root%287%2C81%29\"or approximately 1.873444005\r\n" );
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document.write( "Edwin
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