Question

[Natsu Dragneel Monster End]

cho a,b,c,d là các số không bằng nhau và (a+b+c+d).(a-b-c+d)=(a-b+c-d)(a+b-c-d) chứng minh rằng a:c=b:d

Answer 1

[Phương An]

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

\(\left(a+d\right)^2-\left(b+c\right)^2=\left(a-d\right)^2-\left(b-c\right)^2\)

\(\left(a+d\right)^2-\left(a-d\right)^2=\left(b+c\right)^2-\left(b-c\right)^2\)

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

\(2d\times2a=2b\times2c\)

\(ad=bc\)

\(\frac{a}{c}=\frac{b}{d}\left(\text{đ}pcm\right)\)