Câu hỏi của Online Math

Question

CMR: Nếu $\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}$ thì $\frac{a}{b}=\frac{c}{d}$

Lê Anh Duy · Accepted Answer

Ta có

$\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}\Rightarrow\left(5a+3b\right)\left(5c-3d\right)=\left(5c+3d\right)\left(5a-3b\right)$

$\Rightarrow25ac-15ad+15bc-9bd-25ac+15bc-15ad+9bd=0$

$\Rightarrow-30ad+30bc=0$

$\Rightarrow-30ad=-30bc\Rightarrow ad=bc$

hay $\frac{a}{b}=\frac{c}{d}$ ( ĐPCM)

Câu trả lời: Ta có

$\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}\Rightarrow\left(5a+3b\right)\left(5c-3d\right)=\left(5c+3d\right)\left(5a-3b\right)$

$\Rightarrow25ac-15ad+15bc-9bd-25ac+15bc-15ad+9bd=0$

$\Rightarrow-30ad+30bc=0$

$\Rightarrow-30ad=-30bc\Rightarrow ad=bc$

hay $\frac{a}{b}=\frac{c}{d}$ ( ĐPCM)

Nguyễn Đình Huy · Answer

Ta có

5a+3b5a−3b=5c+3d5c−3d⇒(5a+3b)(5c−3d)=(5c+3d)(5a−3b)5a+3b5a−3b=5c+3d5c−3d⇒(5a+3b)(5c−3d)=(5c+3d)(5a−3b)

⇒25ac−15ad+15bc−9bd−25ac+15bc−15ad+9bd=0⇒25ac−15ad+15bc−9bd−25ac+15bc−15ad+9bd=0

⇒−30ad+30bc=0⇒−30ad+30bc=0

⇒−30ad=−30bc⇒ad=bc⇒−30ad=−30bc⇒ad=bc

hay ab=cdab=cd ( ĐPCM)Câu trả lời: Ta có

5a+3b5a−3b=5c+3d5c−3d⇒(5a+3b)(5c−3d)=(5c+3d)(5a−3b)5a+3b5a−3b=5c+3d5c−3d⇒(5a+3b)(5c−3d)=(5c+3d)(5a−3b)

⇒25ac−15ad+15bc−9bd−25ac+15bc−15ad+9bd=0⇒25ac−15ad+15bc−9bd−25ac+15bc−15ad+9bd=0

⇒−30ad+30bc=0⇒−30ad+30bc=0

⇒−30ad=−30bc⇒ad=bc⇒−30ad=−30bc⇒ad=bc

hay ab=cdab=cd ( ĐPCM)