document.write( "Question 1186258: Solve 3√x + 5/√ x = 16. \n" ); document.write( "
Algebra.Com's Answer #817138 by ikleyn(53751)\"\" \"About 
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\n" ); document.write( "Solve \"3%2Asqrt%28x%29\" + \"5%2Fsqrt%28x%29\" = 16.
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\n" ); document.write( "\n" ); document.write( "            @MathLover1 solved  ANOTHER  equation,  DIFFERENT  from the given in the post.\r
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\n" ); document.write( "\n" ); document.write( "            So her solution and her answer have no any relation to the posed problem.\r
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\n" ); document.write( "\n" ); document.write( "            I came to bring the correct solution.\r
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document.write( "Your starting equation is\r\n" );
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document.write( "    \"3%2Asqrt%28x%29\" + \"5%2Fsqrt%28x%29\" = 16.\r\n" );
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document.write( "Introduce new variable  y = \"sqrt%28x%29\".  Then the given equation takes the form\r\n" );
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document.write( "    3y + \"5%2Fy\" = 16.\r\n" );
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document.write( "Multiply both sides by y.  You will get an EQUIVALENT equation\r\n" );
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document.write( "    3y^2 + 5 = 16y,  \r\n" );
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document.write( "or\r\n" );
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document.write( "    3y^2 - 16y + 5 = 0.\r\n" );
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document.write( "Apply the quadratic formula and find the roots.   They are  y = 5  and  y = \"1%2F3\".\r\n" );
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document.write( "Hence,  for  x = \"y%5E2\",  we have two values  \"5%5E2\" = 25  and  \"%281%2F3%29%5E2\" = \"1%2F9\".\r\n" );
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document.write( "ANSWER.  The given equation has two solutions  x= 25  and/or  x= \"1%2F9\".\r\n" );
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document.write( "You can easily check it by substituting these found values of x into the original equation.\r\n" );
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