Question

Đáp án cũng được, cảm ơn nha

Answer 1

Theo bài ra, ta có:

\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4};a^2+3b^2-2c^2=-16\)

\(\Rightarrow\dfrac{a^2}{2^2}=\dfrac{3b^2}{3.3^2}=\dfrac{2c^2}{2.4^2};a^2+3b^2-2c^2=-16\)

\(\Rightarrow\dfrac{a^2}{4}=\dfrac{3b^2}{27}=\dfrac{2c^2}{32};a^2+3b^2-2c^2=-16\)

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

\(\dfrac{a^2}{4}=\dfrac{3b^2}{27}=\dfrac{2c^2}{32}=\dfrac{a^2+3b^2-2c^2}{4+27-32}=\dfrac{-16}{-1}=16\)

Ta có:

\(\dfrac{a^2}{4}=16\Rightarrow a^2=16.4=64\)

\(\dfrac{3b^2}{27}=16\Rightarrow3b^2=16.27=432\\ \Rightarrow b^2=432:3=144\)

\(\dfrac{2c^2}{32}=16\Rightarrow2c^2=16.32=512\\ \Rightarrow c^2=512:2=256\)

Ta có:

\(H=a^2+b^2+c^2\\ H=64+144+256\\ H=464\)

Vậy: H=464

Answer 2

Ta có:

\(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}\\ \Rightarrow\frac{a^2}{2^2}=\frac{3b^2}{3\cdot3^2}=\frac{2c^2}{2\cdot4^2}\\\Rightarrow\frac{a^2}{4}=\frac{3b^2}{27}=\frac{2c^2}{32} \)

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

\(\frac{a^2}{4}=\frac{3b^2}{27}=\frac{2c^2}{32}=\frac{a^2+3b^2-2c^2}{4+27-32}=\frac{-16}{-1}=16\)

Lại có:

\(\frac{a^2}{4}=16\\ \Rightarrow a^2=16\cdot4\\ \Rightarrow a^2=64\\ \Rightarrow\frac{3b^2}{27}=16\\ \Rightarrow3b^2=16\cdot27\\ \Rightarrow3b^2=432\\ \Rightarrow b^2=\frac{432}{3}\\ \Rightarrow b^2=144\\ \frac{2c^2}{32}=16\\ \Rightarrow2c^2=16\cdot32\\ \Rightarrow2c^2=512\\ \Rightarrow c^2=\frac{512}{2}\\ \Rightarrow c^2=256\)

Vậy \(H=a^2+b^2+c^2=64+14+256=464\)

Answer 3

H=464