document.write( "Question 1151423: 1) suppose (x^2)+(y^2)=1 is a known identity. Determine if, under such assumption, the following is an identity: 2(y^6)+(x^5)=-2(x^6)+(x^5)+6(x^4)-6(x^2)+2
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\n" ); document.write( "2) suppose (x^2)+3=x+1 is a known identity. Determine if, under such assumption, the following is an identity: 6(x^5)+8=-6x+44
\n" ); document.write( "A) NOT an identity
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\n" ); document.write( "Note: can you please give me the answer and explain how did get that answer, I have no idea how to solve this type of questions. Thanks \n" ); document.write( "

Algebra.Com's Answer #773211 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Edwin made a huge and a perfect job solving these problems and explaining it to you.\r\n" );
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document.write( "But I still want to return to the problem.\r\n" );
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document.write( "    - Why ?\r\n" );
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document.write( "Because I think that its formulation is FAR FROM TO BE precisely perfect and correct.\r\n" );
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document.write( "So, I want to concentrate my and your attention on matters that were, probably, out the scope of the visitor, \r\n" );
document.write( "of the author of the problem and even out the Edwin's scope.\r\n" );
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document.write( "What Edwin proved, is THIS:\r\n" );
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document.write( "    If   = 1,     (1)  \r\n" );
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document.write( "        then  \r\n" );
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document.write( "      = .      (2)\r\n" );
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document.write( "Mathematicians express it by these words:\r\n" );
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document.write( "    if  values of x and y satisfy equation (1), then they satisfy also equation (2).\r\n" );
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document.write( "Or by these words: \r\n" );
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document.write( "    if the set of points {(x,y)} satisfy equation (1), then this set of points satisfy equation (2), also.\r\n" );
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document.write( "Or by these words:\r\n" );
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document.write( "    equation (2) is satisfied on the set of solutions of equation (1).\r\n" );
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document.write( "Notice that I do not use the words \r\n" );
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document.write( "    \"the following is an identity   = -2(x^6) + (x^5) + 6(x^4) - 6(x^2) + 2(x^5) + 6(x^4) - 6(x^2) + 2}}}\"    (*)\r\n" );
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document.write( "because the literal meaning of these words is that the identity (*) is true for ALL VALUES of variables x and y.\r\n" );
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document.write( "The last statement, OBVIOUSLY, would be FALSE and WRONG.\r\n" );
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document.write( "So, actually, the correct formulation to problem (1) would be \r\n" );
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document.write( "    Prove that the first given equation is equivalent to the second given equation on the coordinate plane.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Math is a precise science, and it loves those who operates with right ideas and
\n" ); document.write( "use right words to express these ideas.\r
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document.write( "Same or very similar note about the problem (2).\r\n" );
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document.write( "Its correct formulation would be\r\n" );
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document.write( "    Check if the first given equation is equivalent to the second given equation.\r\n" );
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document.write( "Edwin showed that the first given polynomial is a factor to the second given polynomial.\r\n" );
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document.write( "Therefore, every solution to the first polynomial is the solution to the second polynomial.\r\n" );
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document.write( "But the second polynomial has other factor and, via this factor, has other solution, which is not the solution to the first equation.\r\n" );
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document.write( "So, the first and the second given equations ARE NOT EQUIVALENT.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that I do not use the term/terms \"identity\", but use the terms \"equivalent\" or \"not equivalent\", instead,\r
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