Question

cho tỉ lệ thức\(\frac{a}{b}=\frac{c}{d}\)

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

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

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

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

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

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