document.write( "Question 478840: My question is: Solve this equation algebraically \r
\n" ); document.write( "\n" ); document.write( "x^5=3x+2x^3y\r
\n" ); document.write( "\n" ); document.write( "and: Find all the solutions algebraically\r
\n" ); document.write( "\n" ); document.write( "1) Sqroot(x) − Sqroot(x − 5) = 1\r
\n" ); document.write( "\n" ); document.write( "2)3x(x-1)^(1/2)+2(x-1)^(1/2)=0\r
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\n" ); document.write( "\n" ); document.write( "If you can please explain how to solve it for future reference. Thank You :) \n" ); document.write( "
Algebra.Com's Answer #328150 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Solve this equation algebraically
\n" ); document.write( "x^5 = 3x + 2x^3y
\n" ); document.write( "x^5 - 2x^3y = 3x
\n" ); document.write( "Factor out x^3
\n" ); document.write( "x^3(x^2 - 2y) = 3x
\n" ); document.write( "divide both sides by x
\n" ); document.write( "x^2(x^2 - 2y) = 3
\n" ); document.write( "x^2 - 2y = \"3%2Fx%5E2\"
\n" ); document.write( "-2y = \"3%2Fx%5E2\" - x^2
\n" ); document.write( "Divide both sides by -2
\n" ); document.write( "y = \"-3%2F%282x%5E2%29\" + \"x%5E2%2F2\"
\n" ); document.write( "put over a single denominator
\n" ); document.write( "y = \"%28-3+%2B+x%5E4%29%2F%282x%5E2%29\"
\n" ); document.write( "y = \"%28x%5E4-3%29%2F%282x%5E2%29\"
\n" ); document.write( "Solve for x
\n" ); document.write( "\"%28x%5E4-3%29%2F%282x%5E2%29\" = 0
\n" ); document.write( "Divide both sides by 2x^2
\n" ); document.write( "x^4 - 3 = 0
\n" ); document.write( "x^4 = 3
\n" ); document.write( "x = 3^(1/4)
\n" ); document.write( "x = +/- 1.316
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Find all the solutions algebraically
\n" ); document.write( "1) \"sqrt%28x%29+-+sqrt%28x-5%29\" = 1
\n" ); document.write( "Rearrange this to
\n" ); document.write( "\"sqrt%28x%29+-+1+=+sqrt%28x-5%29\"
\n" ); document.write( "Square both sides
\n" ); document.write( "\"%28sqrt%28x%29-1%29%5E2%29\" = x - 5
\n" ); document.write( "FOIL the left side
\n" ); document.write( "x - 2(\"sqrt%28x%29\" + 1 = x - 5
\n" ); document.write( "-2(\"sqrt%28x%29\" = x -x - 5 - 1
\n" ); document.write( "-2(\"sqrt%28x%29\" = -6
\n" ); document.write( "Square both sides again
\n" ); document.write( "4x = 36
\n" ); document.write( "x = \"36%2F4\"
\n" ); document.write( "x = 9
\n" ); document.write( "Check this in the original equation
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "2)\"3x%28x-1%29%5E%281%2F2%29%2B2%28x-1%29%5E%281%2F2%29\"=0
\n" ); document.write( "\"3x%28x-1%29%5E%281%2F2%29\" = \"-2%28x-1%29%5E%281%2F2%29\"
\n" ); document.write( "Square both sides
\n" ); document.write( "9x^2(x-1) = 4(x-1)
\n" ); document.write( "divide both sides by (x-1), leaving us with
\n" ); document.write( "9x^2 = 4
\n" ); document.write( "Find the square root of both sides
\n" ); document.write( "3x = 2
\n" ); document.write( "x = \"2%2F3\", sadly, this will work in the original equation, no solution for x
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