Question

Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}.\)CMR: \(\frac{a^2+b^2}{c^2+d^2}=\left(\frac{a-b}{c-d}\right)^2\)

Answer 1

ĐẶT K NHA

Answer 2

\(Dat:\frac{A}{B}=\frac{C}{D}=k\Rightarrow A=Bk;C=Dk\)

\(\Rightarrow\frac{A^2+B^2}{C^2+D^2}=\frac{B^2\left(k^2+1\right)}{D^2\left(k^2+1\right)}=\frac{B^2}{D^2};\left(\frac{A-B}{C-D}\right)^2=\left(\frac{B\left(k-1\right)}{D\left(k-1\right)}\right)^2=\frac{B^2}{D^2}\Rightarrow dpcm\)

Answer 3

Dặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=bk;c=dk\)

VT : \(\frac{b^2k^2+b^2}{d^2k^2+d^2}=\frac{b^2\left(k^2+1\right)}{d^2\left(k^2+1\right)}=\frac{b^2}{d^2}\left(1\right)\)

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

Từ ( 1 ) và ( 2 ) 

\(\Rightarrow\frac{a^2+b^2}{c^2+d^2}=\left(\frac{a-b}{c-d}\right)^2\)

Study well 

Answer 4

Nhưng mình cần giải theo tính chất dãy tỉ số bằng nhau ấy :(

Answer 5

\(\frac{A}{B}=\frac{C}{D}\Rightarrow\frac{A}{C}=\frac{B}{D}\Rightarrow\frac{A^2}{C^2}=\frac{B^2}{D^2}=\frac{AB}{CD}=\frac{2AB}{2CD}=\frac{A^2+B^2}{C^2+D^2}=\frac{A^2-2AB+B^2}{C^2-2CD+D^2}=\left(\frac{A-B}{C-D}\right)^2\)