document.write( "Question 61754: Find the set of all real solutions. If the solution set contains infinitely many elements, use interval notation to represent it.
\n" ); document.write( " $\"sqrt%282x%2B3%29\"$ - $\"sqrt%28x-2%29\"$ =2 \n" ); document.write( "

Algebra.Com's Answer #42496 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
sqrt(2x+3)-{sqrt(x-2)=2
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "(2x+3)-2sqrt(2x^2-x-6)+x-2=4
\n" ); document.write( "3x+1-2sqrt(2x^2-x-6)=4
\n" ); document.write( "2sqrt(2x^2-x-6)=3x-3
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "4(2x^2-x-6)=9x^2-18x+9
\n" ); document.write( "8x^2-4x-24=9x^2-18x+9
\n" ); document.write( "x^2-14x+15=0
\n" ); document.write( "(x-15)(x+1)=0
\n" ); document.write( "x=15 or x=-1
\n" ); document.write( "Check these to see if they are extraneous.
\n" ); document.write( "Check x=15; OK as both neither integrand is negative.
\n" ); document.write( "Check x=-1; Extraneous as x-2 would be negative.
\n" ); document.write( "Only solution: x=15
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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