document.write( "Question 190040: Solve the rational equation\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2F16=x%5E6%2F2\"$ \n" ); document.write( "

Algebra.Com's Answer #142614 by stanbon(75887) $\"\"$ $\"About$

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Solve the rational equation\r
\n" ); document.write( "\n" ); document.write( "x^3/16 = x^6/2
\n" ); document.write( "---
\n" ); document.write( "Cross-multiply to get:
\n" ); document.write( "2x^3 = 16x^6
\n" ); document.write( "Rearrange:
\n" ); document.write( "16x^6 - 2x^3 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "2x^3(8x^3-1) = 0
\n" ); document.write( "---
\n" ); document.write( "x = 0 or 8x^3-1 = 0
\n" ); document.write( "-------------
\n" ); document.write( "Solve 8x^3-1 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "(2x-1)(4x^2+2x+1) = 0
\n" ); document.write( "x = 1/2 or 4x^2+2x+1 = 0
\n" ); document.write( "-------------
\n" ); document.write( "Sole 4x^2+2x+1 = 0
\n" ); document.write( "x = [-2 +- sqrt(4 - 4*4*1)]/2
\n" ); document.write( "x = [-2 +- sqrt(-12)]/2
\n" ); document.write( "x = [-2 +- 2isqrt(3)]/2
\n" ); document.write( "x = [-1 +- isqrt(3)]
\n" ); document.write( "--------------------------
\n" ); document.write( "Ans: x = -1+sqrt(3)i, x = -1-sqrt(3)i, x = 1/2 , x = 0 (multiplicity 3) \n" ); document.write( "

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