document.write( "Question 364906: 2x^2/3 - 8x^1/3 + 15 = 0\r
\n" ); document.write( "\n" ); document.write( "Thanks for your help and time!!! \n" ); document.write( "

Algebra.Com's Answer #260166 by Jk22(389) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2x%5E2%2F3+-+8x%5E1%2F3+%2B+15+=+0\"$ | let $\"x+=+y%5E3\"$
\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( " $\"2%28y-2%29%5E2+=+-7\"$ , negative hence there are no real solutions
\n" ); document.write( "
\n" ); document.write( "(Or discriminant = 8^2 - 4*15*2 < 0)\r
\n" ); document.write( "\n" ); document.write( "the complex solutions are : y = 2 +/- i*Sqrt(7/2)
\n" ); document.write( "
\n" ); document.write( "and x = [2 +/- i*Sqrt(7/2)]^(1/3)
\n" ); document.write( "
\n" ); document.write( "to put x on the form a + ib, for example : |y| = Sqrt(4 + 7/2) = Sqrt(15/2)
\n" ); document.write( "
\n" ); document.write( "writing then : y = |y|exp(it), we find t = atg(7/8)
\n" ); document.write( "
\n" ); document.write( "y^(1/3)=Sqrt(15/2)^(1/3)*exp(it/3 + 2*pi/3 *m), m=0, 1, 2
\n" ); document.write( " \n" ); document.write( "

\n" );