document.write( "Question 1123954: While doing his homework, Bryan thought about the football game, which is why he made a mistake. Instead of raising a number to the second power, he doubled it and got a two-digit number; this was the reverse of the correct answer. What was the correct answer? \n" ); document.write( "

Algebra.Com's Answer #740327 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        In Math, I know \"an opposite number\" - it is \" -x \", the number with the opposite sign.\r
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\n" ); document.write( "\n" ); document.write( "        I also know \"an inverse number\" - it is    $\"1%2Fx\"$ .\r
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\n" ); document.write( "\n" ); document.write( "        But I don't know what \"the reverse number\" means.\r
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\n" ); document.write( "\n" ); document.write( "If it is the number with reversed digits, then the solution is as follows.\r
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document.write( "Let  x is the original number, which is  under the question.\r\n" );
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document.write( "It is clear that under given condition, x is one-digit number.\r\n" );
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document.write( "Then  2x = 10a + b,  the two-digit number with the \"tens\" digit \"a\" and the \"ones\" digit \"b\".\r\n" );
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document.write( "The condition says\r\n" );
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document.write( "    2x = 10a + b,  while  x^2 = 10b + a.\r\n" );
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document.write( "       T A B L E \r\n" );
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document.write( "  x   2x= 10a+b      x^2= 10b+a\r\n" );
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document.write( "  1      2\r\n" );
document.write( "  2      4\r\n" );
document.write( "  3      6\r\n" );
document.write( "  4      8             16\r\n" );
document.write( "  5     10             25\r\n" );
document.write( "  6     12             36\r\n" );
document.write( "  7     14             49\r\n" );
document.write( "  8     16             64\r\n" );
document.write( "  9     18             81\r\n" );
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document.write( "From the Table, you see that \r\n" );
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document.write( "    (a)  2x is a two-digits number only for  5 <= x <= 9,   and\r\n" );
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document.write( "    (b)  in this case,  the \"tens\" digit of 2x is 1.\r\n" );
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document.write( "         It means that x^2 has the \"ones\" digit 1. \r\n" );
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document.write( "The only square of an integer number between 5 and 9, which is ended by 1, is 9.\r\n" );
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document.write( "And this number, x= 9, satisfies all the conditions.\r\n" );
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document.write( "Answer.  x = 9.\r\n" );
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