a) Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\)
\(\dfrac{a}{b}=\dfrac{3a}{3b}\) ; \(\dfrac{c}{d}=\dfrac{2c}{2d}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a+c}{b+d}=\dfrac{3a+2c}{3b+2d}\)
\(\Rightarrow\dfrac{a}{b}=\dfrac{3a+2c}{3b+2d}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) Chứng minh rằng \(\dfrac{ac}{bd}=\dfrac{a^2+c^2}{b^2+d^2}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)
CMR: \(\dfrac{a^2+ac}{c^2-ac}=\dfrac{b^2+bd}{d^2-bd}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) chứng minh
d) \(\dfrac{2a+5b}{3a-4b}=\dfrac{2c+5d}{3c-4d}\)
e) \(\dfrac{2016a-2017b}{2017c+2018d}=\dfrac{2016c-2017d}{2017a+2018b}\)
g) \(\dfrac{7a^2+5ac}{7a^2-5ac}=\dfrac{7b^2+5ab}{7b^2-5ab}\)
Cho các số a,b,c,d thỏa mãn \(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}.\) Chứng minh rằng: ad=bc hoặc ac=bd
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) CMR:
a) \(\left(\dfrac{a-b}{c-d}\right)^4=\dfrac{a^4+b^4}{c^4+d^4}\)
b) \(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)
c) \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)
bài 2
Cho \(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\) chứng minh \(\dfrac{a}{b}=\dfrac{c}{d}\) hoặc \(\dfrac{a}{b}=\dfrac{d}{c}\)
Bài 1: Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) chứng minh rằng :
a, \(\dfrac{a+b}{b}=\dfrac{c+d}{d}\)
b, \(\dfrac{a^2-b^{2^{ }}}{c^2-d^2}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
Cho a, b, c>0 và\(\dfrac{2b+c-a}{a}=\dfrac{2c-b+a}{b}=\dfrac{2a+b-c}{c}\)
Tính Q=\(\dfrac{\left(3a-2b\right)\left(3b-2c\right)\left(3c-2a\right)}{\left(3a-c\right)\left(3b-a\right)\left(3c-b\right)}\)
Help!!!
Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\) chứng minh \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
