document.write( "Question 1210378: Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
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Algebra.Com's Answer #852138 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "x+y = 10
\n" ); document.write( "(x+y)^3 = 10^3
\n" ); document.write( "x^3+3x^2y+3xy^2+y^3 = 1000 .......... binomial theorem
\n" ); document.write( "(x^3+y^3) + (3x^2y+3xy^2) = 1000
\n" ); document.write( "(x^3+y^3) + 3xy(x+y) = 1000
\n" ); document.write( "300+3xy(10) = 1000 ............. plug in x+y=10 and x^3+y^3=300
\n" ); document.write( "300+30xy = 1000
\n" ); document.write( "30xy = 1000-300
\n" ); document.write( "30xy = 700
\n" ); document.write( "xy = 700/30
\n" ); document.write( "xy = 70/3\r
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\n" ); document.write( "\n" ); document.write( "x+y = 10
\n" ); document.write( "x(x+y) = 10x ...... multiplying both sides by x
\n" ); document.write( "x^2+xy = 10x
\n" ); document.write( "x^2+70/3 = 10x ........... plug in xy = 70/3 found earlier
\n" ); document.write( "3x^2+70 = 30x ........... multiply both sides by the LCD 3
\n" ); document.write( "3x^2-30x+70 = 0
\n" ); document.write( "I'll let the student finish up.
\n" ); document.write( "I recommend using the quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( "You should get two distinct real number solutions for x.
\n" ); document.write( "Once determining x, you can determine the paired value of y.\r
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\n" ); document.write( "\n" ); document.write( "Due to symmetry, if (a,b) is a solution then (b,a) is the other solution.
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