document.write( "Question 252851: One positive number is 5 more than another. The sum of their squares is 53. Find BOTH numbers and solve algebraically. \n" ); document.write( "

Algebra.Com's Answer #184946 by richwmiller(17219) $\"\"$ $\"About$

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x=y+5
\n" ); document.write( "x^2+y^2=53
\n" ); document.write( "They must be rather small numbers if their sum is 53 since 7^2=49
\n" ); document.write( "and it just so happens that 2 and 7 are the numbers
\n" ); document.write( "2^2+7^2=53
\n" ); document.write( "7-2=5
\n" ); document.write( "so now you have 4the equations to solve it and the answers.
\n" ); document.write( "there is a good chance that you can factor the equation
\n" ); document.write( "just plug y+5 in for x in the equation x^2+y^2=53
\n" ); document.write( "(y+5)^2+y^2=53
\n" ); document.write( "y^2+10y+25+y^2=53
\n" ); document.write( "2y^2+10y-28=0
\n" ); document.write( "divide by 2
\n" ); document.write( "y2+5y-14=0
\n" ); document.write( "Yes it can be factored
\n" ); document.write( "(y+7)(y-2)==
\n" ); document.write( "y=-7
\n" ); document.write( "y=2
\n" ); document.write( "discard the -7 since we need a positive result
\n" ); document.write( "x=y+5
\n" ); document.write( "x=7
\n" ); document.write( "we already showed that 2 and 7 work
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