\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\\ \Rightarrow\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{c^2}{16}\\ =\dfrac{a^2+3b^2-2c^2}{4+27-32}=-\dfrac{16}{-1}=16\\ \Rightarrow a=\pm8;b=\pm12;c=\pm16\)
Ta có: \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\)
\(\Rightarrow\dfrac{a^2}{4}=\dfrac{3b^2}{27}=\dfrac{2c^2}{32}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\dfrac{a^2}{4}=\dfrac{3b^2}{27}=\dfrac{2c^2}{32}=\dfrac{a^2+3b^2-2c^2}{4+27-32}=\dfrac{-16}{-1}=16\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{a^2}{4}=16\Rightarrow a=8\\\dfrac{3b^2}{27}=16\Rightarrow b=12\\\dfrac{2c^2}{32}=16\Rightarrow c=16\end{matrix}\right.\)
Ta có :
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\Rightarrow\) \(\dfrac{a^2}{2^2}=\dfrac{3b^2}{3.3^2}=\dfrac{2c^2}{2.4^2}\Rightarrow\dfrac{a^2}{4}=\dfrac{3b^2}{27}=\dfrac{2c^2}{32}\)
và a2 + 3b2 - 2c2 = -16
Áp dụng tính chất của dãy tỉ số bằng nhau ,có :
\(\dfrac{a^2}{4}=\dfrac{3b^2}{27}=\dfrac{2c^2}{32}\Rightarrow\dfrac{a^2+3b^2-2c^2}{4+27-32}=\dfrac{-16}{-1}=16\)
\(a^2=16\cdot4=64\Rightarrow a=8\)
\(3b^2=16\cdot27=432\Rightarrow b^2=\dfrac{432}{3}=144\Rightarrow b=12\)
\(2c^2=16\cdot32=\text{ }512\Rightarrow c^2=\dfrac{512}{2}=256\Rightarrow c=16\)
Vậy a = 8 ; b = 12 ; c = 16
