document.write( "Question 1111149: $\"+2%5E%28x%2B1%29%2B2%5Ex=3%5E%28y%2B2%29-3%5Ey+\"$ , x, y ∈ Z. Find x. \n" ); document.write( "

Algebra.Com's Answer #726167 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "One solution is  x = 3,  y = 1.\r\n" );
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document.write( "Then your equation takes the form\r\n" );
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document.write( "2^4 + 2^3 = 3^3 - 3^1,    and it is true, because each side is equal to 24.\r\n" );
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document.write( "    Next statement is that  there is NO any other solution.\r\n" );
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document.write( "You can easily prove it on your own, based on this notices:\r\n" );
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document.write( "    - the left side of the given equation is   =  =   and has \"3\" as a factor in degree 1;\r\n" );
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document.write( "    - the right side of the given equation is   =  and has  \"3\" as a factor in degree \"y\".\r\n" );
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document.write( "Hence,  y = 1,   and the rest is easy.\r\n" );
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