document.write( "Question 280834: The sum of two numbers is seven. The sum of the squares of the two numbers is twenty-nine. Find the two numbers. \n" ); document.write( "

Algebra.Com's Answer #204083 by oberobic(2304) $\"\"$ $\"About$

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x + y = 7
\n" ); document.write( "x = 7-y
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\n" ); document.write( "x^2 + y^2 = 29
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\n" ); document.write( "(7-y)^2 + y^2 = 29
\n" ); document.write( "(7-y)(7-y) +y^2 = 29
\n" ); document.write( "49 -7y - 7y + y^2 + y^2 = 29
\n" ); document.write( "2y^2 -14y + 49 = 29
\n" ); document.write( "2y^2 - 14y + 49 - 29 = 0
\n" ); document.write( "2y^2 - 14y + 20 = 0
\n" ); document.write( "y^2 - 7y + 10 = 0
\n" ); document.write( "(y-2)(y-5) = 0
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\n" ); document.write( "y=2 OR y=5
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\n" ); document.write( "But it is possible that one of these is NOT an answer.
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\n" ); document.write( "Checking...
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\n" ); document.write( "x+y = 7
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\n" ); document.write( "Substituting y = 2, then x = 5
\n" ); document.write( "2^2 = 4
\n" ); document.write( "5^2 = 25
\n" ); document.write( "4+25 = 29
\n" ); document.write( "So, y=2 and x=5 is a solution.
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\n" ); document.write( "Substituting y=5, then x = 2.
\n" ); document.write( "That works too.
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\n" ); document.write( "Answer:
\n" ); document.write( "The two numbers are 2 and 5.
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\n" ); document.write( "Done \n" ); document.write( "

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