document.write( "Question 100012: The difference of two positive numbers is 2 and the sum of their squares is 74. Find the numbers \n" ); document.write( "
Algebra.Com's Answer #72965 by ankor@dixie-net.com(22740)\"\" \"About 
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\"The difference of two positive numbers is 2\"
\n" ); document.write( "one number = x
\n" ); document.write( "another number = (x+2)
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\n" ); document.write( "\"the sum of their squares is 74.\"
\n" ); document.write( " x^2 + (x+2)^2 = 74
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\n" ); document.write( " x^2 + (x^2 + 4x + 4) = 74; FOILed (x+2)*(x+2)
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\n" ); document.write( "2x^2 + 4x + 4 - 74 = 0
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\n" ); document.write( "2x^2 + 4x - 70 = 0; a quadratic equation
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\n" ); document.write( "x^2 + 2x - 35; simplified, divided by 2
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\n" ); document.write( "Factors to:
\n" ); document.write( "(x + 7) (x - 5) = 0
\n" ); document.write( "x = +5, they want the positive number, the other number would be 7
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\n" ); document.write( "Check: 5^2 + 7^2 = 74; confirms our solution\r
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