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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: tìm các số a,b,c biết rằng ab=c, bc=4a, ac=9b

Toán Lớp 7: tìm các số a,b,c biết rằng ab=c, bc=4a, ac=9b

$a =b = c = 0 \quad |\quad a = ±3 ; b = ±2 ; c = ±6$
$\begin{array}{l} \text{Từ}\ \begin{cases} ab =c \\ bc = 4a \\ ac = 9b \end{cases} \\ \Rightarrow ab . bc . ac = c . 4a . 9b \Rightarrow (abc)^2 = 36abc \\ \Rightarrow (abc)^2 – 36(abc) =0 \\ \Rightarrow (abc)(abc – 36) =0 \Rightarrow \left[\begin{matrix} abc =0 \\ abc -36 =0\end{matrix}\right. \\ \Rightarrow \left[\begin{matrix} abc =0 \\ abc =36\end{matrix}\right. \\ \Rightarrow \left[\begin{matrix} abc =0 \\ abc =36\end{matrix}\right. \\ \text{Xét trường hợp :}\ abc =0 \\ \Rightarrow \left[\begin{matrix} a=0 \\ b =0 \\c =0\end{matrix}\right. \\ \text{Xét trường hợp:}\ abc =36 \\ \Rightarrow c . c =36 \Rightarrow c^2 =36 \Rightarrow c = 6 \text{ hoặc}\ c = -6 \\ \text{ Lại có:} \\ \Rightarrow abc =36 \Rightarrow a . 4a = 4a^2= 36 \Rightarrow a^2 =9 \Rightarrow a = 3 \text{ hoặc } a = -3 \\ \text{Tương tự:} \\ \Rightarrow abc =36 \Rightarrow 9b . b =9b^2 =36 \Rightarrow b^2 =4 \Rightarrow b = 2 \\\text{ hoặc } b = -2 \\ \text{Vậy } a =b = c = 0 \quad |\quad a = ±3 ; b = ±2 ; c = ±6 \\ \end{array}$
$a=\pm3,b=\pm2,c=\pm6$.
$ab.\!bc.\!ac=c.\!4a.\!9b\\\Rightarrow abc.\!abc=36abc\\\Rightarrow abc=36\\\Rightarrow\dfrac{abc}{ab}=\dfrac{36}c\\\Rightarrow c=\dfrac{36}c\\\Rightarrow c^2=36\\\Rightarrow c^2=6^2=\left(-6\right)^2\\\Rightarrow c=\pm6\\\Rightarrow \dfrac{abc}{bc}=\dfrac{36}{4a}\\\Rightarrow a=\dfrac9a\\\Rightarrow a^2=9\\\Rightarrow a^2=3^2=\left(-3\right)^2\\\Rightarrow a=\pm3\\\Rightarrow\dfrac{abc}{ac}=\dfrac{36}{9b}\\\Rightarrow b=4b\\\Rightarrow b^2=4\\\Rightarrow b^2=2^2=\left(-2\right)^2\\\Rightarrow b=\pm2$
Vậy $a=\pm3,b=\pm2,c=\pm6$.