Algebra.Com's Answer #846626 by ikleyn(52776)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "a + b + c = 6
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document.write( "a² + b² + c² = 14,
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document.write( "find the value of a⁸ + b⁸ + c⁸
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document.write( "It is assumed that a, b, c are integer numbers.\r\n" );
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document.write( "From  +  +  = 14 we guess one solution\r\n" );
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document.write( " a= 3, b= 2, c= 1.\r\n" );
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document.write( "Indeed, then\r\n" );
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document.write( " 3 + 2 + 1 = 6\r\n" );
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document.write( "and\r\n" );
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document.write( " 3^2 + 2^2 + 1^2 = 9 + 4 + 1 = 14.\r\n" );
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document.write( "So, (a,b,c) = (3,2,1) is the basic solution.\r\n" );
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document.write( "There are 5 other solutions that are permutations of the basic triple.\r\n" );
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document.write( "But we should not worry about permutations, since they do not make influence on\r\n" );
document.write( "the sum  +  +  .\r\n" );
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document.write( "Also, it is clear from the equation for squares, that there are no other solutions in integer numbers.\r\n" );
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document.write( "Now we make direct calculation + + =  +  +  = 6818.\r\n" );
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document.write( "ANSWER. Under given conditions, the sum + + is 6818.\r\n" );
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document.write( "Solved.\r
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document.write( "Happy learning (1)\r
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document.write( "Come again to this forum soon for new knowledge !\r
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