Question

cho a/b=c/d chứng minh:(a-b)^2/(c-d)^2=a.d/c.d

Answer 1

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

=>a=bk; c=dk

\(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{\left(bk-b\right)^2}{\left(dk-d\right)^2}=\frac{b^2\left(k-1\right)^2}{d^2\left(k-1\right)^2}=\frac{b^2}{d^2}\)

\(\frac{ab}{cd}=\frac{bk\cdot b}{dk\cdot d}=\frac{b^2}{d^2}\)

Do đó: \(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{ab}{cd}\)