document.write( "Question 41306: Find Positive Root: $\"+2x%5E-1%2B+%28x-1%29%5E-1=4+\"$ \n" ); document.write( "

Algebra.Com's Answer #26678 by Earlsdon(6294) $\"\"$ $\"About$

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Find the positive root:
\n" ); document.write( " $\"2x%5E-1+%2B+%28x-1%29%5E-1+=+4\"$ Simplify.
\n" ); document.write( " $\"2%2Fx+%2B+1%2F%28x-1%29+=+4\"$ Add the fractions on the left side.
\n" ); document.write( " $\"%282%28x-1%29+%2B+x%29%2F%28x%28x-1%29%29+=+4\"$ Simplify.
\n" ); document.write( " $\"%283x-2%29%2F%28x%5E2-x%29+=+4\"$ Multiply both sides by x^2-x
\n" ); document.write( " $\"3x-2+=+4%28x%5E2-x%29\"$ Simplify.
\n" ); document.write( " $\"3x-2+=+4x%5E2-4x\"$ Subtract 3x-2 from both sides.
\n" ); document.write( " $\"4x%5E2-7x%2B2+=+0\"$ } Solve the quadratic equation by the quadratic formula: $\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-%28-7%29%2B-sqrt%28%28-7%29%5E2-4%284%29%282%29%29%29%2F2%284%29\"$ Simplify.
\n" ); document.write( " $\"x+=+%287%2B-sqrt%2849-32%29%29%2F8\"$
\n" ); document.write( " $\"x+=+%287%2B-sqrt%2817%29%29%2F8\"$ \r
\n" ); document.write( "\n" ); document.write( "One positive root is:
\n" ); document.write( " $\"x+=+%287%2F8%29%2B%28sqrt%2817%29%29%2F8\"$ = 1.40 (approximately)\r
\n" ); document.write( "\n" ); document.write( "The other positive root is:
\n" ); document.write( " $\"x+=+%287%2F8%29-%28sqrt%2817%29%29%2F8\"$ = 0.36 (approximately) \n" ); document.write( "

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