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You can put this solution on YOUR website!
Let x = \"one number\"
\n" ); document.write( "Let y = \"another number\"
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\"One number is 2 greater than another number.\"
\n" ); document.write( "x = y + 2
\n" ); document.write( ":
\n" ); document.write( "\"the sum of their squares is 5 times the square of the smaller number,\"
\n" ); document.write( "x^2 + y^2 = 5y^2
\n" ); document.write( "x^2 = 5y^2 - y^2
\n" ); document.write( "x^2 = 4y^2
\n" ); document.write( ":
\n" ); document.write( "What are the numbers?
\n" ); document.write( "From the 1st statement we know x = (y+2)
\n" ); document.write( "replace x with (y+2)
\n" ); document.write( "(y+2)^2 = 4y^2
\n" ); document.write( "FOIL
\n" ); document.write( "y^2 + 4x + 4 = 4y^2
\n" ); document.write( "Arrange as a quadratic on the right
\n" ); document.write( "0 = 4y^2 - y^2 - 4x - 4
\n" ); document.write( "0 = 3y^2 - 4y - 4
\n" ); document.write( "Factor this to
\n" ); document.write( "(3y + 2)(y - 2) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "3y = -2
\n" ); document.write( "y =
\n" ); document.write( "and
\n" ); document.write( "y = 2
\n" ); document.write( ":
\n" ); document.write( "Find x when y = -2/3
\n" ); document.write( "x =
\n" ); document.write( "x =
\n" ); document.write( ":
\n" ); document.write( "Find x when y = 2
\n" ); document.write( "x = 2 + 2
\n" ); document.write( "x = 4
\n" ); document.write( ":
\n" ); document.write( "x = 4, y = 2 and x = 4/3, y = -2/3
\n" ); document.write( ":
\n" ); document.write( "You should check both solutions in: x^2 + y^2 = 5y^2 \n" ); document.write( "