document.write( "Question 851069: Find three consecutive numbers, the sum of whose squares is 29 more than three times the square of the smallest. \n" ); document.write( "
Algebra.Com's Answer #512568 by JulietG(1812)\"\" \"About 
You can put this solution on YOUR website!
Here's what we know from the problem:
\n" ); document.write( "A = B-1
\n" ); document.write( "B = C-1 (therefore C = A+2, B = A+1)
\n" ); document.write( "a^2 + b^2 + c^2 = 29 + 3a^2
\n" ); document.write( ".
\n" ); document.write( "Let's replace the values in the bottom equation with the equivalents we know.
\n" ); document.write( "a^2 + (a+1)^2 + (a+2)^2 = 29 + 3a^2
\n" ); document.write( "Square out the parentheses
\n" ); document.write( "a^2 + (a^2 + 2a + 1) + (a^2 + 4a + 4) = 29 + 3a^2
\n" ); document.write( "Add
\n" ); document.write( "3a^2 + 6a + 5 = 29 + 3a^2
\n" ); document.write( "Subtract 3a^2 from each side
\n" ); document.write( "6a + 5 = 29
\n" ); document.write( "Subtract 5 from each side
\n" ); document.write( "6a = 24
\n" ); document.write( "Divide each side by 6
\n" ); document.write( "a = 4
\n" ); document.write( ".
\n" ); document.write( "If a is 4, then b is 5, and c is 6
\n" ); document.write( ".
\n" ); document.write( "Let's plug it in \"the sum of whose squares is 29 more than three times the square of the smallest.\"
\n" ); document.write( "4^2 + 5^2 +6^2 = 29 + (3*4^2)
\n" ); document.write( "16 + 25 + 36 = 29 + 48
\n" ); document.write( "41 + 36 = 77
\n" ); document.write( "77 = 77
\n" ); document.write( "Success!
\n" ); document.write( " \n" ); document.write( "
\n" );