document.write( "Question 1031967: (2x+5)^4+(2x+1)^4=82 [Hint: Put (2x+3)=y] \n" ); document.write( "
Algebra.Com's Answer #646649 by Edwin McCravy(20056)\"\" \"About 
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document.write( "\"%282x%2B5%29%5E4%2B%282x%2B1%29%5E4=82\" [Hint: Put (2x+3)=y]\r\n" );
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document.write( "Using the hint 2x+3=y, then 2x=y-3.  \r\n" );
document.write( "Substitute y-3 for 2x:\r\n" );
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document.write( "\"%28y-3%2B5%29%5E4%2B%28y-3%2B1%29%5E4=82\"\r\n" );
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document.write( "\"%28y%2B2%29%5E4%2B%28y-2%29%5E4=82\"\r\n" );
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document.write( "Multiply that out and collect terms:\r\n" );
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document.write( "\"2y%5E4%2B48y%5E2%2B32=82\"\r\n" );
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document.write( "\"2y%5E4%2B48y%5E2-50=0\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"y%5E4%2B24y%5E2-25=0\"\r\n" );
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document.write( "\"%28y%5E2-1%29%28y%5E2%2B25%29=0\"\r\n" );
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document.write( "\"%28y-1%29%28y%2B1%29%28y%5E2-25i%5E2%29=0\"\r\n" );
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document.write( "\"%28y-1%29%28y%2B1%29%28y-5i%29%28y%2B5i%29=0\"\r\n" );
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document.write( "y=1, y=-1, y=5i, y=-5i\r\n" );
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document.write( "Since 2x+3=y\r\n" );
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document.write( "2x+3=1, 2x+3=-1, 2x+3=5i, 2x+3=-5i\r\n" );
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document.write( "2x=-2, 2x=-4, 2x=-3+5i, 2x=-3-5i\r\n" );
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document.write( "x=-1, x=-2, x=-3/2+5/2i, x=-3/2-5/2i\r\n" );
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document.write( "Edwin
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