document.write( "Question 441834: Solve:
\n" ); document.write( "sq rt of 3x-5 - sq rt of x+2 = 1 \n" ); document.write( "

Algebra.Com's Answer #304866 by htmentor(1343) $\"\"$ $\"About$

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First, square both sides:
\n" ); document.write( " $\"%28sqrt%283x-5%29+-+sqrt%28x%2B2%29%29%5E2+=+1%5E2\"$
\n" ); document.write( "Applying FOIL on the LHS we have:
\n" ); document.write( " $\"%283x-5%29+%2B+%28x%2B2%29+-+2sqrt%28%283x-5%29%28x%2B2%29%29+=+1\"$
\n" ); document.write( "Collecting terms and isolating the term with the square root gives:
\n" ); document.write( " $\"4x-4+=+2sqrt%28%283x-5%29%28x%2B2%29%29\"$
\n" ); document.write( "Isolating the square root term allows us to square both sides again:
\n" ); document.write( " $\"%284x-4%29%5E2+=+4%283x-5%29%28x%2B2%29\"$
\n" ); document.write( "Performing the multiplcation gives:
\n" ); document.write( " $\"16x%5E2+-32x+%2B+16+=+4%283x%5E2+%2B+x+-+10%29\"$
\n" ); document.write( "Divide through by 4 and collect terms:
\n" ); document.write( " $\"x%5E2+-+9x+%2B+14+=+0\"$
\n" ); document.write( "Solve for x using the quadratic formula:
\n" ); document.write( " $\"x+=+%289+%2B-+sqrt%2881-56%29%29%2F2\"$ -> x = 2, 7
\n" ); document.write( "The squaring operation allows for positive and negative solutions, but only one value of x will make the original expression valid.
\n" ); document.write( "Check:
\n" ); document.write( "x=2: $\"sqrt%286-5%29+-+sqrt%284%29+=+1+-+2+=+-1\"$ [Discard this solution]
\n" ); document.write( "x=7: $\"sqrt%2821-5%29+-+sqrt%289%29+=+4+-+3+=+1\"$ [Correct]
\n" ); document.write( "Ans: x = 7 \n" ); document.write( "

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