document.write( "Question 325633: Find five consecutive intgers if the square of the first less the square of the third is 5 less than the sum of the fourth and the fifth intgers. \n" ); document.write( "

Algebra.Com's Answer #233160 by jessica43(140) $\"\"$ $\"About$

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To solve this problem, we need to write an equation using the information provided in the equation.
\n" ); document.write( "First, you have five consecutive integers:
\n" ); document.write( "x, x+1, x+2, x+3, x+4 (where x = the first integer)
\n" ); document.write( "Second, we know the square of the first less the square of the third is 5 less than the sum of the fourth and the fifth intgers. This can be written as:
\n" ); document.write( "x^2 - (x+2)^2 = ((x+3)+(x+4)) - 5
\n" ); document.write( "Now we can solve for x:
\n" ); document.write( "x^2 - (x+2)^2 = ((x+3)+(x+4)) - 5
\n" ); document.write( "x^2 - (x+2)^2 = (2x + 7)- 5
\n" ); document.write( "x^2 - (x+2)^2 = 2x + 2
\n" ); document.write( "x^2 - (x+2)(x+2) = 2x + 2
\n" ); document.write( "x^2-x^2+4x+4 = 2x + 2
\n" ); document.write( "4x + 4 = 2x + 2
\n" ); document.write( "2x +4 = 2
\n" ); document.write( "2x = -2
\n" ); document.write( "x = -1
\n" ); document.write( "So the first integer in the series is -1. So the five consecutive integers are -1, 0, 1, 2, 3 \n" ); document.write( "

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