Question

Cho \(\frac{a}{b}=\frac{c}{d}\) Chứng Minh

1 \(\frac{a^2+b^2}{a^2-b^2}=\frac{c^2+d^2}{c^2-d^2}\)

Answer 1

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

\(\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}\)

Áp dụng tinhd chất dãy tỉ số bằng nhau ta có:

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

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