Question

[Nguyễn Thị Thùy Linh]

cho a/b = c/d ; c khác o

 CMR(a-b/c-d)^2 =ab/cd

(a+b/c+d)^3=(a^3-b^3)/(c^3-d^3)

Answer 1

[Nguyễn Linh Chi]

Ta co: \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\)

=> \(\frac{a}{c}.\frac{b}{d}=\frac{a-b}{c-d}.\frac{b}{d}=\frac{a-b}{c-d}.\frac{a-b}{c-d}\)

=>. \(\frac{ab}{cd}=\left(\frac{a-b}{c-d}\right)^2\)

Ta co: \(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\)

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