Odpowiedź:
a,b,c geometryczny
a, b+2 ,c+1 arytmetyczny
[tex]a+b+c=21\\b+2-a=c+1-(b+2)\quad \Rightarrow\quad 2b=c+a-3\quad \Rightarrow\quad c+a=2b+3\\(a+c)+b=21\quad \Rightarrow\quad 2b+3+b=21\quad \Rightarrow\quad 3b=18/:3\quad \Rightarrow\quad b=6\\\left\{\begin{array}{llc}a+c+6=21\\ac=6^2\end{array} \right\\\left\{\begin{array}{llc}a+c=15\\ac=36\end{array} \right\\\left\{\begin{array}{llc}c=15-a\\a(15-a)=36\end{array} \right\\\left\{\begin{array}{llc}c=15-a\\15a-a^2=36\end{array} \right\\a^{2} -15a+36=0\\[/tex]
[tex]\Delta=15^2-4*36=81\quad \sqrt{\Delta} =9\\\displaystyle a_1=\frac{15-9}{2} =3\quad a_2=\frac{15+9}{2} =12\\c_1=15-a_1=12\quad c_2=15-a_2=3\\a=3\quad b=6\quad c=12\quad \lor\quad a=12\quad b=6\quad c=3\\\text{rosnacy}\quad \underline {a=3\quad b=6 \quad c=12}[/tex]
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Odpowiedź:
a,b,c geometryczny
a, b+2 ,c+1 arytmetyczny
[tex]a+b+c=21\\b+2-a=c+1-(b+2)\quad \Rightarrow\quad 2b=c+a-3\quad \Rightarrow\quad c+a=2b+3\\(a+c)+b=21\quad \Rightarrow\quad 2b+3+b=21\quad \Rightarrow\quad 3b=18/:3\quad \Rightarrow\quad b=6\\\left\{\begin{array}{llc}a+c+6=21\\ac=6^2\end{array} \right\\\left\{\begin{array}{llc}a+c=15\\ac=36\end{array} \right\\\left\{\begin{array}{llc}c=15-a\\a(15-a)=36\end{array} \right\\\left\{\begin{array}{llc}c=15-a\\15a-a^2=36\end{array} \right\\a^{2} -15a+36=0\\[/tex]
[tex]\Delta=15^2-4*36=81\quad \sqrt{\Delta} =9\\\displaystyle a_1=\frac{15-9}{2} =3\quad a_2=\frac{15+9}{2} =12\\c_1=15-a_1=12\quad c_2=15-a_2=3\\a=3\quad b=6\quad c=12\quad \lor\quad a=12\quad b=6\quad c=3\\\text{rosnacy}\quad \underline {a=3\quad b=6 \quad c=12}[/tex]