Giải
Theo bài ra ta có:
\(b^2=ac\Rightarrow\)\(\dfrac{a}{c}=\dfrac{b}{b}\Rightarrow\)\(\Rightarrow\dfrac{a}{b}=\dfrac{b}{c}\Rightarrow\dfrac{a^2}{b^2}=\dfrac{b^2}{c^2}=\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a^2.b^2}{b^2.c^2}=\dfrac{a}{b}.\dfrac{b}{c}=\dfrac{a}{c}\)
\(\Rightarrow\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)
Bai 1: Cho a2=b.c. Chứng minh: \(\dfrac{a^2+c^2}{a^2+b^2}=\dfrac{c}{d}\)
Bài 2: Cho: \(^{\dfrac{a}{b}=\dfrac{b}{c}}\). Chứng minh: \(\dfrac{a^2-b^2}{b^2-c^2}\)=\(\dfrac{a}{c}=\dfrac{\left(a-b\right)^2}{\left(b-c\right)^2}\)
GIÚP KHẨN CẤP NHA !
Cho \(\dfrac{a}{b}=\dfrac{c}{d} \) . Chứng minh :
a, \(\dfrac{a^2+c^2}{b^2+d^2} =\dfrac{ac}{bd}\)
b, \(\dfrac{a^2+c^2}{b^2+d^2} = \dfrac{a^2-c^2}{b^2-d^2}\)
c, \(\dfrac{(a+c)^2}{(b+d)^2} = \dfrac{(a-c)^2}{b-d)^2}\)
d, \(\dfrac{a^2+b^2}{a^2-b^2} = \dfrac{c^2+d^2}{c^2-d^2}\)
e, \(\dfrac{(a-b )^2}{(c-d)^2} = \dfrac{a^2+b^2}{c^2+d^2}\)
cho a/b=c/d khac 1 va a,b,c,d khac 0. chung minh (a-b)^2/(c-d)^2=ab/cd
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 \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh rằng ta có các tỉ lệ thức sau (giả thiết các tỉ lệ thức là có nghĩa ) :
a) \(\dfrac{ab}{cd}=\dfrac{a^2-b^2}{c^2-d^2}\)
b) \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
1) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh rằng \(\dfrac{2a^2-3ab+5b^2}{2a^2+3ab}=\dfrac{2c^2-3cd+5d^2}{2c^2+3cd}\)
2) Cho \(\dfrac{a}{c}=\dfrac{c}{b}\). Chứng minh rằng \(\dfrac{b^2-c^2}{a^2+c^2}=\dfrac{b-a}{a}\)
3) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\).Chứng minh rằng\(\dfrac{3a^6+c^6}{3b^6+d^6}=\dfrac{\left(a+c\right)^6}{\left(b+d\right)^6}\)
Cho : \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) ( a,b,c,d khác 0)
\(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
Cho A=\(\dfrac{28a^2-3ab-2008b^2}{11c^2-9cd-1985d^2}\)
Tính A biết: \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}\)với a,b,c,d thuộc R và a,b,c,d khác 0
Bài 1: CMR : Nếu a2 = b.c thì \(\dfrac{a+b}{a-b}=\dfrac{c+a}{c-a}\) Đảo lại có đúng không?
Bài 2: Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) CMR: \(\left(\dfrac{a+b+c}{b+c+d}\right)\)3 =\(\dfrac{a}{d}\)
Bài 3: Cho dãy tỉ số: \(\dfrac{b.z-c.y}{a}=\dfrac{c.x-a.z}{b}=\dfrac{a.y-b.x}{c}\) , CMR: \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\)
