Question

CMR:

(a+c)(b-d)=(a-c)(b+d)

Answer 1

Ta có:

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

\(\Rightarrow\left(a+c\right)\left(b-d\right)=\left(a-c\right)\left(b+d\right)\)(đpcm)

Answer 2

Theo t/c của dãy tỉ số = nhau, ta có

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

\(\Rightarrow\left(a+c\right)\left(b-d\right)=\left(b+d\right)\left(a-c\right)\)

Vậy \(\left(a+c\right)\left(b-d\right)=\left(a-c\right)\left(b+d\right)\)\(\left(dpcm\right)\)