Question

cho 3 so tu nhien lien tiep.Lap cac tich cua 2 trong 3 so do va biet tong cua ba tich nay la 242 .hay tim 3 so do ???

Answer 1

gọi 3 stn liên tiếp đó là a;a+1;a+2

\(\Rightarrow a\left(a+1\right)+a\left(a+2\right)+\left(a+1\right)\left(a+2\right)=242\)

\(\Rightarrow a^2+a+a^2+2a+a^2+2a+a+2=3a^2+6a+2=242\)

\(\Rightarrow3a^2+6a+3=243\Rightarrow3\left(a^2+2a+1\right)=3\left(a+1\right)^2=243\Rightarrow\left(a+1\right)^2=81\)

\(\Rightarrow a+1=9\Rightarrow a=8\Rightarrow a+2=8+2=10\)

vậy 3 số đó là 8;9;10