atuftofwisps
atuftofwisps atuftofwisps
  • 07-01-2017
  • Mathematics
contestada

Find three consecutive even numbers if it is known that the sum of the squares of the first 2 is equal to the square of the third number.

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konrad509
konrad509 konrad509
  • 07-01-2017
[tex](2n)^2+(2n+2)^2=(2n+4)^2\\ 4n^2+4n^2+8n+4=4n^2+16n+16\\ 4n^2-8n-12=0\\ 4(n^2-2n-3)=0\\ n^2-2n-3=0\\ n^2+n-3n-3=0\\ n(n+1)-3(n+1)=0\\ (n-3)(n+1)=0\\ n=3 \vee n=-1\\\\ \underline{n=3}\\ 2n=6\\ 2n+2=8\\ 2n+4=10\\\\ \underline{n=-1}\\ 2n=-2\\ 2n+2=0\\ 2n+4=2[/tex]

6,8,10 or -2,0,2
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