Đặt a/b=c/d=k
=>k2=a2/b2=c2/d2=a2+c2/b2+d2 (1)
a/b=c/d=>a/c=b/d
=>k2=k.k=a/c.b/d=ab/cd (2)
Từ (1) và (2) ta có
a2+c2/b2+d2=ab/cd (đpcm)
tick cho minh nha mình đang cần điểm
Cho : \(\frac{a}{b}=\frac{c}{d}CMR:\)\(\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}v\text{à}\left(\frac{a+b}{c+d}\right)^2=\frac{a^2+b^2}{c^2+d^2}\)
Cho \(\frac{a}{b}=\frac{c}{d}\). CMR:
a) \(\frac{a^2-b^2}{c^2-d^2}=\frac{ab}{cd}\)
b) \(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{ab}{cd}\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}.CMR:\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}\)
cho tỉ lệ thức : \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}cmr\frac{a}{b}=\frac{c}{d}\)
Cho\(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)
CMR:\(\frac{a}{b}=\frac{c}{d}\)hoặc \(\frac{a}{b}=\frac{d}{c}\)
Cho:
\(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}.CMR:\frac{a}{b}=\frac{c}{d}\)
CMR nếu \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)(a,b,c,d khác 0). CMR \(\frac{a}{b}=\frac{c}{d}\)hoặc \(\frac{a}{b}=\frac{d}{c}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)CMR \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)
Cho \(\frac{a}{b}=\frac{c}{d}\), CMR:
a) \(\frac{a^2-b^2}{c^2-d^2}=\frac{ab}{cd}\)
b)\(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{ab}{cd}\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)CMR
\(\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}\)và \(\left(\frac{a+b}{c+d}\right)^2=\frac{a^2+b^2}{c^2+d^2}\)
