Câu hỏi của Jackson Roy

Question

$\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}$ va a2 + b2 - 2c2 = -76 . tim a,b,c

$\dfrac{x}{5}=\dfrac{2y}{7}$ và x - y = 11 .tìm x , y

ル・ジア・バオ · Accepted Answer

Ta có: $\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\Rightarrow\left(\dfrac{a}{2}\right)^2=\left(\dfrac{b}{3}\right)^2=\left(\dfrac{c}{4}\right)^2$

$\Rightarrow\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{z^2}{16}$$\Rightarrow\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{2c^2}{32}$

Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:

$\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{2c^2}{32}=\dfrac{a^2+b^2-2c^2}{4+9-32}=\dfrac{-76}{-19}=4$

$\Rightarrow\dfrac{a^2}{4}=4\Rightarrow a=4$

$\dfrac{b^2}{9}=4\Rightarrow b=6$

$\dfrac{2c^2}{32}=4\Rightarrow2c^c=128\Rightarrow c=8$

Vậy $\left\{{}\begin{matrix}a=4\b=6\c=8\end{matrix}\right.$Câu trả lời: Ta có: $\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\Rightarrow\left(\dfrac{a}{2}\right)^2=\left(\dfrac{b}{3}\right)^2=\left(\dfrac{c}{4}\right)^2$