Bài tập về chứng minh tỉ lệ thức

5. $\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$

$\Rightarrow \frac{a^{3}}{b^{3}}=\frac{b^{3}}{c^{3}}=\frac{c^{3}}{d^{3}}=\frac{a^{3}+b^{3}+c^{3}}{b^{3}+c^{3}+d^{3}}$

Mà $\frac{a^{3}}{b^{3}}=\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\frac{a}{d}$

Do đó $\frac{a^{3}+b^{3}+c^{3}}{b^{3}+c^{3}+d^{3}}=\frac{a}{d}$

6. $\frac{2a+15b}{5a-7b}=\frac{2c+15d}{5c-7d}$

$\Rightarrow $ (2a+15b).(5c-7d)=(2c+15d).(5a-7b)

$\Leftrightarrow $ 10ac + 75bc - 14ad - 105bd = 10ac + 75ad - 14bc - 105bd

$\Leftrightarrow $ ad = bc

$\Leftrightarrow \frac{a}{b}=\frac{c}{d}$