document.write( "Question 313304: two positive integers with a difference of six. if the smaller is added to the square of the larger the sum is 84. what are the two integers? \n" ); document.write( "

Algebra.Com's Answer #224045 by moshiz08(60) $\"\"$ $\"About$

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Let's call the bigger integer $\"x\"$ and the smaller integer $\"y\"$ . \r
\n" ); document.write( "\n" ); document.write( "The difference is six. In an equation, this means $\"+x+-+y+=+6+\"$ . Another way to write this is: $\"+y+=+x+-+6+\"$ . \r
\n" ); document.write( "\n" ); document.write( "if the smaller $\"y\"$ is added to the square of the larger $\"x%5E2\"$ the sum is 84: this means $\"+y+%2B+x%5E2+=+84+\"$ . \r
\n" ); document.write( "\n" ); document.write( "Let's substitute our expression for $\"+y+\"$ into this equation. Then we have \r
\n" ); document.write( "\n" ); document.write( " $\"+y+%2B+x%5E2+=+%28+x+-+6%29+%2B+x%5E2+=+84+\"$ \r
\n" ); document.write( "\n" ); document.write( "so subtracting 84 from both sides gives: $\"+x%5E2+%2B+x+-+90+=+0+\"$ . \r
\n" ); document.write( "\n" ); document.write( "Now we can factor: $\"+x%5E2+%2B+x+-+90+=+%28x+-+9%29+%2A+%28x+%2B+10%29+=+0\"$ . Therefore, there are two solutions: $\"+x+=+9\"$ or $\"x+=+-10\"$ . Since the integer must be positive, we know our answer is $\"+x+=+9\"$ . \r
\n" ); document.write( "\n" ); document.write( "Now we can find $\"y\"$ from the fact that the difference is 6: $\"+x+-+y+=+9+-+y+=+6\"$ implies that $\"y+=+3\"$ . \r
\n" ); document.write( "\n" ); document.write( "So we have the solution x = 9, y = 3. \n" ); document.write( "

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