Question

Tìm a, b, c biết : \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}\)và \(a^2-b^2+2c^2=108\)

Answer 1

a/2=b/3=c/4

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

 

Answer 2

\(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}\)

\(\Rightarrow\frac{a^2}{2^2}=\frac{b^2}{3^2}=\frac{2c^2}{2.4^2}=\frac{a^2-b^2+2c^2}{4-9+32}=\frac{108}{27}=4\)

=> \(\frac{a^2}{4}=4\Rightarrow a^2=16\Rightarrow a=+-4\)

=> \(\frac{b^2}{9}=4\Rightarrow b^2=36\Rightarrow b=+-6\)

=>\(\frac{2c^2}{2.4^2}=4\Rightarrow c^2=16.4=64\Rightarrow c=+-8\)

Answer 3

ta có \(\frac{a^2}{4}=\frac{b^2}{9}=\frac{c^2}{16}=\frac{2c^2}{32}\)

\(TTCDTSBN,ta\)\(có\)

\(\frac{a^2}{4}=\frac{b^2}{9}=\frac{2c^2}{32}=\frac{a^2-b^2+2c^2}{4-9+32}=\frac{108}{27}=4\)

\(\frac{a^2}{4}=4\Rightarrow a^2=16\Rightarrow a=4\)

\(\frac{b^2}{9}=4\Rightarrow b^2=36\Rightarrow b=6\)

\(\frac{c^2}{16}=4\Rightarrow c^2=64\Rightarrow c=8\)

a,b,c cùng dấu

Answer 4

a = + 4

b = +  6

c = + 8