Question

Biết a/a'=b/b'=c/c'=4 và a'+b'+c' khác 0 , a'-3b'+2c' khác 0

Tính :

a, a+b+c/a'+b'+c'

b,a-3b+2c/a'-3b'+2c'

Answer 1

a) Vì \(\dfrac{a}{a'}=\dfrac{b}{b'}=\dfrac{c}{c'}=4\)

\(\Rightarrow\left\{{}\begin{matrix}a=4a'\\b=4b'\\c=4c'\end{matrix}\right.\)

\(\Rightarrow\dfrac{a+b+c}{a'+b'+c'}=\dfrac{4a'+4b'+4c'}{a'+b'+c'}\)\(=\dfrac{4\left(a'+b'+c'\right)}{a'+b'+c'}=4\)

b)\(\Rightarrow\dfrac{a-3b+2c}{a'-3b'+2c'}=\dfrac{4a'-3\cdot4b'+2\cdot4c'}{a'-3b'+2c'}\)\(=\dfrac{4a'-12b'+8c'}{a'-3b'+2c'}\)\(=\dfrac{4\left(a'-3b'+2c'\right)}{a'-3b'+2c'}=4\)