\(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow\dfrac{a^2}{b^2}=\dfrac{c^2}{d^2}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a^2}{b^2}=\dfrac{c^2}{d^2}=\dfrac{a^2-c^2}{b^2-d^2}\left(1\right)\)
\(\dfrac{a^2}{b^2}=\dfrac{c^2}{d^2}=\dfrac{a^2+c^2}{b^2+d^2}\left(2\right)\)
Từ (1) và (2) ta có đpcm
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh rằng
a) \(\dfrac{ab}{cd}=\dfrac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)
Chứng minh rằng từ tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\) (b, d ≠ 0) ta suy ra được các tỉ lệ thức:
a/ \(\dfrac{a+b}{a-b}=\dfrac{c+d}{c-d}\)
b/ \(\dfrac{a}{a+b}=\dfrac{c}{c+d}\)
c/ \(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)
d/ \(\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{ac}{bd}\)
e/ \(\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{a^2-c^2}{b^2-d^2}\)
f/ \(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}=\dfrac{a^2+b^2}{c^2+d^2}\)
Cho tỉ lệ thức \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) Chứng minh:
1)\(\dfrac{a-b}{b}\)=\(\dfrac{c-d}{d}\) 2)\(\dfrac{a-b}{a}\)=\(\dfrac{c-d}{c}\)
giải giúp mk vss
Biết \(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\) với a,b,c,d khác 0. Chứng minh rằng: \(\dfrac{a}{b}=\dfrac{c}{d}\) hoặc \(\dfrac{a}{b}=\dfrac{d}{c}\)
Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}.\) Chứng minh rằng ta có tỉ lệ thức sau: \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\)
chứng minh
a. \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
b. \(\dfrac{a\cdot b}{c\cdot d}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
c.\(\dfrac{2008\cdot a-2009\cdot b}{2009\cdot c+2010\cdot d}=\dfrac{2008\cdot c-2009\cdot d}{2009\cdot a+2010\cdot b}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh rằng:
a)\(\dfrac{2a+3b}{2a-3b}=\dfrac{2c+3d}{2c-3d}\)
b) \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
cho \(\dfrac{a}{b}\) =\(\dfrac{c}{d}\) cm rằng
a) \(\dfrac{a}{a-b}\) =\(\dfrac{c}{c-d}\) b)\(\dfrac{a}{b}\) =\(\dfrac{a+c}{b+d}\) c) \(\dfrac{a}{3a+d}\) =\(\dfrac{c}{3c+d}\) d)\(\dfrac{a.c}{b.d}\) =\(\dfrac{a^2+c^2}{b^2+c^2}\) e)\(\dfrac{a.b}{c.d}\) =\(\dfrac{a^2-b^2}{c^2-d^2}\) f)\(\dfrac{a.b}{c.d}\) =\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
mn giúp mk vs ạ! thanks
Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh :
a) \(\dfrac{3a+5b}{2a-7b}=\dfrac{3c+5d}{2c-7d}\)
b) \(\dfrac{\left(a+b\right)^2}{\left(c+d\right)^2}=\dfrac{ab}{cd}\)
