Question

cho a/b=c/d CMR 

a)ab/cd=(a^2+b^2)/(c^2+d^2)

Answer 1

Gọi a/b=c/d=k nên a=bk; c=dk

nên \(\frac{ab}{cd}=\frac{bk\cdot b}{dk\cdot d}=\frac{b^2\cdot k}{d^2\cdot k}=\frac{b^2}{d^2}\)(1)

nên \(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(bk\right)^2+b^2}{\left(dk\right)^2+d^2}=\frac{b^2\cdot k^2+b^2}{d^2\cdot k^2+d^2}=\frac{b^2\left(k^2+1\right)}{d^2\left(k^2+1\right)}=\frac{b^2}{d^2}\)(2)

Từ (1);(2) => ab/cd=(a^2+b^2)/(c^2+d^2)

Answer 2

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

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