document.write( "Question 974618: The sum of the squares of two consective positive integers is 61. Find these two numbers \n" ); document.write( "

Algebra.Com's Answer #596484 by algebrahouse.com(1659) $\"\"$ $\"About$

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x = first consecutive positive integer
\n" ); document.write( "x + 1 = second consecutive positive integer\r
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\n" ); document.write( "\n" ); document.write( "x² + (x + 1)² = 61 {sum of squares of two consecutive positive integers is 61}
\n" ); document.write( "x² + (x + 1)(x + 1) = 61 {when squaring a binomial, multiply it by itself}
\n" ); document.write( "x² + x² + 2x + 1 = 61 {used the foil method}
\n" ); document.write( "2x² + 2x + 1 = 61 {combined like terms}
\n" ); document.write( "2x² + 2x - 60 = 0 {subtracted 61 from each side}
\n" ); document.write( "2(x² + x - 30) = 0 {factored a 2 out}
\n" ); document.write( "x² + x - 30 = 0 {set each factor equal to 0, 2 cannot be equal to 0}
\n" ); document.write( "(x + 6)(x - 5) = 0 {factored into two binomials}
\n" ); document.write( "x + 6 = 0 or x - 5 = 0 {set each factor equal to 0}
\n" ); document.write( "x = -6 or x = 5 {solved each equation for x}
\n" ); document.write( "x + 1 = -5 or x + 1 = 6 {substituted -6 and 5, in for x, into x + 1}\r
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\n" ); document.write( "\n" ); document.write( "5 and 6
\n" ); document.write( "are the two consecutive positive integers
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