document.write( "Question 62177: SQRT(3X+1) - SQRT (X-1)= 2, SOLVE COULD BE 2 ANSWERS \n" ); document.write( "

Algebra.Com's Answer #42932 by joyofmath(189) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%283x%2B1%29+-+sqrt%28x-1%29=+2\"$ \r
\n" ); document.write( "\n" ); document.write( "Add sqrt(x-1) to both sides: $\"sqrt%283x%2B1%29+=+2%2Bsqrt%28x-1%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "Square both sides: $\"3x%2B1+=+%282%2Bsqrt%28x-1%29%29%5E2\"$ .
\n" ); document.write( "Or, $\"3x%2B1+=+4%2B4sqrt%28x-1%29%2Bx-1\"$ .
\n" ); document.write( "Combine like terms: $\"2x-2+=+4sqrt%28x-1%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "Square both sides: $\"%282x-2%29%5E2+=+%284sqrt%28x-1%29%29%5E2\"$ .
\n" ); document.write( "Or, $\"4x%5E2-8x%2B4+=+16%28x-1%29+=+16%28x-1%29+=+16x+-+16\"$ .
\n" ); document.write( "So, $\"4x%5E2-24x%2B20+=+0\"$ .
\n" ); document.write( "Divide the whole equation by 4: $\"x%5E2-6x%2B5+=+0\"$ .
\n" ); document.write( "Factor the equation: $\"%28x-5%29%28x-1%29+=+0\"$ so $\"x=5\"$ or $\"x=1\"$ .\r
\n" ); document.write( "\n" ); document.write( "Verify: \r
\n" ); document.write( "\n" ); document.write( "When x=5, $\"sqrt%283x%2B1%29-sqrt%28x-1%29+=+sqrt%2816%29-sqrt%284%29=4-2\"$ which is indeed 2.
\n" ); document.write( "When x=1, $\"sqrt%283x%2B1%29-sqrt%28x-1%29+=+sqrt%284%29-sqrt%280%29+=+2\"$ . \n" ); document.write( "

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