document.write( "Question 1055142: x^2 - 6x- (x^2 -6x - 3 )^1/2 =5 \n" ); document.write( "

Algebra.Com's Answer #670376 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "x^2 - 6x- (x^2 -6x - 3 )^1/2 =5
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document.write( "x^2 - 6x- (x^2 -6x - 3 )^1/2 =5 --->\r\n" );
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document.write( "(x^2 - 6x -3) - (x^2 -6x - 3 )^1/2 = 2.   (*)\r\n" );
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document.write( "Introduce new variable \r\n" );
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document.write( "u = (x^2 -6x - 3 )^1/2.\r\n" );
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document.write( "Then the equation (*) takes the form\r\n" );
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document.write( "u^2 - u = 2,   or\r\n" );
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document.write( "u^2 - u - 2 = 0.\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "(u-2)*(u+1) = 0.\r\n" );
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document.write( "The roots are u = 2  and  u = -1.\r\n" );
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document.write( "Now you have this equations for x:\r\n" );
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document.write( "     (x^2 -6x - 3 )^1/2 = 2  --->  x^2 -6x - 3 = 4  --->  x^2 -6x -7 = 0.\r\n" );
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document.write( "     Factor: (x-7)*(x+1) = 0  --->  the roots are x= 7 and x= -1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Plot y = $\"x%5E2+-+6x-+%28x%5E2+-6x+-+3+%29%5E%281%2F2%29\"$ and y = 5\r
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