document.write( "Question 72601: I am kind of stuck on this problem... maybe someone can assist me! any help would be greatly appreciated!\r
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\n" ); document.write( "\n" ); document.write( " For the equation x - √x = 0, perform the following:
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\n" ); document.write( "\n" ); document.write( "b) Graph the functions y = x and y = √x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.\r
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\n" ); document.write( "\n" ); document.write( "c) How does the graph relate to part a?
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Algebra.Com's Answer #51902 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

I am kind of stuck on this problem...\r\n" );
document.write( "maybe someone can assist me! any help \r\n" );
document.write( "would be greatly appreciated! \r\n" );
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document.write( "For the equation x - Öx = 0, perform \r\n" );
document.write( "the following:\r\n" );
document.write( "a) Solve for all values of x that satisfies \r\n" );
document.write( "the equation.\r\n" );
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document.write( "  x - Öx = 0\r\n" );
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document.write( "Isolate the radical term:\r\n" );
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document.write( "       x = Öx \r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "             _\r\n" );
document.write( "    (x)² = (Öx)² \r\n" );
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document.write( "      x² = x\r\n" );
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document.write( "Get 0 on the right:\r\n" );
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document.write( "  x² - x = 0\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "x(x - 1) = 0\r\n" );
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document.write( "Set each factor = 0:\r\n" );
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document.write( "x = 0,  x - 1 = 0\r\n" );
document.write( "            x = 1\r\n" );
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document.write( "Now we must check these answers in\r\n" );
document.write( "the original equation:\r\n" );
document.write( "       _\r\n" );
document.write( "  x - Öx = 0\r\n" );
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document.write( "Checking x = 0\r\n" );
document.write( "       _\r\n" );
document.write( "  0 - Ö0 = 0  \r\n" );
document.write( "   0 - 0 = 0\r\n" );
document.write( "       0 = 0\r\n" );
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document.write( "Checking x = 1    \r\n" );
document.write( "       _\r\n" );
document.write( "  x - Öx = 0\r\n" );
document.write( "       _\r\n" );
document.write( "  1 - Ö1 = 0\r\n" );
document.write( "   1 - 1 = 0\r\n" );
document.write( "       0 = 0\r\n" );
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document.write( "b) Graph_the functions y = x and\r\n" );
document.write( "   y = Öx on the same graph \r\n" );
document.write( "(by plotting points if necessary). \r\n" );
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document.write( "Show the points of intersection of these two graphs. \r\n" );
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document.write( "The green line is the graph_of y = x and the blue \r\n" );
document.write( "curve is the graph of y = Öx.\r\n" );
document.write( "They intersect at the two points (0,0) and (1,1).\r\n" );
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document.write( "c) How does the graph relate to part a?\r\n" );
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document.write( "If you wanted to find the points where the green line\r\n" );
document.write( "crosses the blue curve, you would solve the system:\r\n" );
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document.write( "y = x_\r\n" );
document.write( "y = Öx\r\n" );
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document.write( "If you subtract the equations you get\r\n" );
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document.write( "0 = x - Öx\r\n" );
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document.write( " or\r\n" );
document.write( "     _\r\n" );
document.write( "x - Öx = 0\r\n" );
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document.write( "which is the original equation\r\n" );
document.write( "Then you would solve that as above and get\r\n" );
document.write( "x = 0, x = 1. Then you would substitute\r\n" );
document.write( "these in one of the equations of the\r\n" );
document.write( "system above and get y = 0, and y = 1\r\n" );
document.write( "respectively. So the two points where\r\n" );
document.write( "the blue curve and and green line intersect\r\n" );
document.write( "are at (0, 0) and (1, 1).\r\n" );
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document.write( "Edwin

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