document.write( "Question 1161693: The line 5x-5y=2 touches the curve x^2y-5x+y+2=0, find the coordinates of the points of intersection. Find the gradient at each of the points \n" ); document.write( "
Algebra.Com's Answer #785293 by Alan3354(69443)\"\" \"About 
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The line 5x-5y=2 touches the curve x^2y-5x+y+2=0, find the coordinates of the points of intersection. Find the gradient at each of the points
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\n" ); document.write( "5x-5y=2
\n" ); document.write( "Solve for y
\n" ); document.write( "y = (5x-2)/5
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\n" ); document.write( "x^2y-5x+y+2=0
\n" ); document.write( "Sub for y
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\n" ); document.write( "x^2*(5x-2)/5 - 5x + (5x-2)/5 + 2 = 0
\n" ); document.write( "Multiply by 5
\n" ); document.write( "x^2*(5x-2) - 25x + (5x-2) + 10 = 0
\n" ); document.write( "5x^3 - 2x^2 -20x + 8 = 0
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\n" ); document.write( "Solve for x
\n" ); document.write( "x = 2 is a root
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\n" ); document.write( "x = -2 is a root
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\n" ); document.write( "x = 0.4 is a root
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\n" ); document.write( "f(x) = 5x^3 - 2x^2 -20x + 8
\n" ); document.write( "f'(x) = 15x^2 - 4x - 20
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\n" ); document.write( "Sub for x at the 3 roots and find the 3 slopes.\r
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