Ta co :\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\)=>\(\left(\dfrac{a}{b}\right)^3=\left(\dfrac{b}{c}\right)^3=\left(\dfrac{c}{d}\right)^3\)
=> \(\dfrac{a^3}{b^3}=\dfrac{b^3}{c^3}=\dfrac{c^3}{d^3}=\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}\) (1)
Mặt khác:\(\dfrac{a^3}{b^3}=\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}=\dfrac{a}{d}\) (2)
Tu (1) va (2)
=> \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\) (dpcm)
Cho \(\dfrac{a}{b}\) = \(\dfrac{b}{c}\) = \(\dfrac{c}{d}\) chung minh rang \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}\) = \(\dfrac{a}{d}\)
Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\). Chứng minh rằng :
\(\dfrac{a}{b}=\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=(\dfrac{a+b-c}{b+c-d})^3\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh :
a, \(\dfrac{a^3+b^3}{c^3+d^3} = \dfrac{a^3-b^3}{c^3-d^3}\)
b, \(\dfrac{(a+b)^3}{(c+d)^3}=\dfrac{a^3+b^3}{c^3+d^3}\)
c, \(\dfrac{(a-b)^3}{(c-d)^3}=\dfrac{3a^2+2b^2}{3c^2+2d^2}\)
d, \(\dfrac{4a^4+5b^4}{4c^4+5d^4}=\dfrac{a^2b^2}{c^2d^2}\)
e, \(\dfrac{a^{10}+b^{10}}{(a+b)^{10}} = \dfrac{c^{10}+d^{10}}{(c+d)^{10}}\)
a) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) (\(a,b,c,d\ne0\)). Chứng minh rằng:
1) \(\dfrac{2a+5b}{3a-4b}=\dfrac{2c+5d}{3c-4d}\)
2) \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)
3) \(\dfrac{a^3+b^3}{c^3+d^3}=\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}\) \(\left(\dfrac{a}{b}=\dfrac{c}{d}\ne1\right)\)
b)Cho \(\dfrac{2a+13b}{3a-7b}=\dfrac{2c+13d}{3c-7d}\). Chứng minh rằng:\(\dfrac{a}{b}=\dfrac{c}{d}\)
c)Cho \(\dfrac{cy-bz}{x}=\dfrac{az-cx}{y}=\dfrac{bx-ay}{z}\). Chứng minh rằng: \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)
cho a, b ,c ,d thoa man \(^{b^2=ac}\)\(^{c^2=bd}\)chung minh \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
Cho tỉ lệ thức :\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) Chứng minh rằng :\(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
Các bạn giúp mình nhanh cho đến 3:50 nhé mình cần gấp
Cho : \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) ( a,b,c,d khác 0 )
Chứng minh :
\(\left(\dfrac{a+b}{c+d}\right)^3\)= \(\dfrac{a^3-b^3}{c^3-d^3}\)
Bài 3:
a. Cho \(\dfrac{a}{c}=\dfrac{c}{b}=\dfrac{b}{d}\) . Chứng minh rằng : \(\dfrac{a^{3^{ }}+c^3-b^3}{c^3+b^3-d^3}=\dfrac{a}{d}\)
b. Tìm số nguyên x, y biết: 42-3 |y−3|= 4(2012-x4)
Bài 1
CMR: \(\dfrac{a}{c}=\dfrac{c}{b}=\dfrac{b}{d}cmr:\dfrac{a^3+c^3-b^3}{c^3+b^3-d^3}=\dfrac{a}{d}\)
