document.write( "Question 248047: the difference of two positive numbers is 3 and the sum of their square is 45. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #180799 by stanbon(75887) $\"\"$ $\"About$

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the difference of two positive numbers is 3 and the sum of their squares is 45. Find the numbers.
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\n" ); document.write( "Equations:
\n" ); document.write( "x - y = 3
\n" ); document.write( "x^2 + y^2 = 45
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\n" ); document.write( "x = y+3
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\n" ); document.write( "Substitute for \"x\" and solve for \"y\":
\n" ); document.write( "(y+3)^2 + y^2 = 45
\n" ); document.write( "y^2 + 6y + 9 + y^2 = 45
\n" ); document.write( "2y^2 + 6y - 36 = 0
\n" ); document.write( "y^2 + 3y - 18 = 0
\n" ); document.write( "(y+6)(y-3) = 0
\n" ); document.write( "y = 3 or y = -6
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\n" ); document.write( "If y = 3, x-3 = 3, x = 6
\n" ); document.write( "If y = -6, x --6 = 3, x = -3
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\n" ); document.write( "Checking x^2 + y^2 = 45
\n" ); document.write( "3^2 + 6^2 = 9 + 36 = 45
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\n" ); document.write( "Solutions:
\n" ); document.write( "x=6 and y = 3
\n" ); document.write( "OR
\n" ); document.write( "x = -3 and y = -6
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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