document.write( "Question 766155: 1...The sum of the squares of two numbers is 4 and the product of them is 1. Find those two numbers.
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Algebra.Com's Answer #466707 by suruman(21)\"\" \"About 
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Let the numbers be x and y.
\n" ); document.write( "Given :
\n" ); document.write( "x^2 + y^2 = 4 ....(a)
\n" ); document.write( "x*y=1 ....(b)
\n" ); document.write( "Multiplying equation 'b' by 2 on L.H.S and R.H.S,
\n" ); document.write( "2*x*y = 2 ....(c)
\n" ); document.write( "adding (a) and (c),
\n" ); document.write( "x^2 + 2*x*y + y^2 = 6
\n" ); document.write( "(x + y)^2 = 6
\n" ); document.write( "x + y = sqrt(6) (Taking only the positive square root. if x+y is taken as -sqrt(6), values of x and y would interchange.)\r
\n" ); document.write( "\n" ); document.write( "y = sqrt(6) - x
\n" ); document.write( "Thus, x*(sqrt(6) -x ) = 1 (since product of the numbers equals 1).
\n" ); document.write( "x*sqrt(6) - x^2 = 1
\n" ); document.write( "x^2 - sqrt(6)*x + 1 = 0
\n" ); document.write( "Roots of the quadratic equation of the type
\n" ); document.write( "a*x^2 + b*x + c = 0 is given by :
\n" ); document.write( "x = ((-b +- sqrt(b^2 - 4*a*c))/(2*a))\r
\n" ); document.write( "\n" ); document.write( "Thus, x = (sqrt(6) + sqrt(2))/2 or (sqrt(6) - sqrt(2))/2
\n" ); document.write( "y = (sqrt(6) - sqrt(2))/2 or (sqrt(6) + sqrt(2))/2\r
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