Question

Nếu\(\frac{a}{b}=\frac{c}{d}\)thì:

\(\left(\frac{a+b}{c+d}\right)^3=\frac{a^3+b^3}{c^{3+}d^3}\)

Answer 1

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)\(\left(k\in Z\right)\)

\(\Rightarrow a=bk,c=dk\)

Có :

\(\left(\frac{a+b}{c+d}\right)^3=\frac{\left(bk+b\right)^3}{\left(dk+d\right)^3}=\frac{\left[b\left(k+1\right)\right]^3}{\left[d\left(k+1\right)\right]^3}=\frac{b^3\left(k+1\right)^3}{d^3\left(k+1\right)^3}=\frac{b^3}{d^3}\)

\(\frac{a^3+b^3}{c^3+d^3}=\frac{\left(bk\right)^3+b^3}{\left(dk\right)^3+d^3}=\frac{b^3k^3+b^3}{d^3k^3+d^3}=\frac{b^3\left(k^3+1\right)}{d^3\left(k^3+1\right)}=\frac{b^3}{d^3}\)

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

Vậy ...

Answer 2

a/b = c/d =K ( K thuộc N* )

a = bK 

c = dK

thay vào 2 cái cần so sanh đó là ok

k cho mik nha

Answer 3

Ta có:

a/b=c/d => a/c=b/d = (a+b)/(c+d)=> (a/c)³=(b/d)³=(\(\frac{a+b}{c+d}\) )³   (1)

Lại có: (a/c)³=(b/d)³ = a³/c³ = b³/d³ =  \(\frac{a^3+b^3}{c^3+d^3}\)

Vậy  (\(\frac{a+b}{c+d}\) )³  = \(\frac{a^3+b^3}{c^3+d^3}\)