Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)

Chứng minh rằng \(\left(\dfrac{a+b}{c+a}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

\(\left(\dfrac{a+b}{c+d}\right)^2=\left(\dfrac{bk+b}{dk+d}\right)^2=\dfrac{b^2}{d^2}\)

\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{b^2k^2+b^2}{d^2k^2+d^2}=\dfrac{b^2}{d^2}\)

Do đó: \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)