Question

Cho tỉ lệ thức a/b =c/d (b+d khác 0) a) 5a^5+c^5/5b^5+d^5 =(a+c)^5/(b+d) ^5

Answer 1

\(\dfrac{a}{b}=\dfrac{c}{d}\rightarrow\dfrac{5a^5}{5b^5}=\dfrac{c^5}{d^5}=\dfrac{5a^5+c^5}{5b^5+d^5}\)

\(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a+c}{b+d}\)

\(\dfrac{a^5}{b^5}=\dfrac{c^5}{d^5}=\dfrac{\left(a+c\right)^5}{\left(b+d\right)^5}\)

nên ta có

\(\dfrac{5a^5+c^5}{5b^5+d^5}=\dfrac{\left(a+c\right)^5}{\left(b+d\right)^5}\)