document.write( "Question 519917: find two consecutive positive integers such that the square of the smaller is one more than eight times the larger. \n" ); document.write( "

Algebra.Com's Answer #345856 by oberobic(2304) $\"\"$ $\"About$

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Two consecutive positive integers are defined by:
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\n" ); document.write( "x+1
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\n" ); document.write( "x^2 = 8(x+1) +1
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\n" ); document.write( "x^2 = 8x +8 +1
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\n" ); document.write( "x^2 -8x -9 = 0
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\n" ); document.write( "(x +1)(x -9) = 0
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\n" ); document.write( "x = -1 or 9
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\n" ); document.write( "Since we are limited to positive integers, which is 9.
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\n" ); document.write( "Answer: The two consecutive positive integers are 9 and 10.
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\n" ); document.write( "Check the answer.
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\n" ); document.write( "9^2 = 81
\n" ); document.write( "8*10+1 = 81
\n" ); document.write( "correct
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\n" ); document.write( "Done. \n" ); document.write( "

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