(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.
(1/a + 1/b + 1/c)2 = 1/a2 + 1/b2 + 1/c2 + 2(1/ab + 1/bc + 1/ac) = 4
<=> 1/a2 + 1/b2 + 1/c2 + 2(bcac + abac + abbc)/(a2b2c2) = 4
<=> 1/a2 + 1/b2 + 1/c2 + 2abc(a + b + c)/(a2b2c2) = 4
<=> 1/a2 + 1/b2 + 1/c2 + 2 = 4
(vì abc(a + b + c) = a2 b2 c2)
<=> 1/a2 + 1/b2 + 1/c2 = 2
câu 11:
\(Cho:\dfrac{1}{c}=\dfrac{1}{2}\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\left(vớia,b,c\ne0;b\ne c\right)\)
\(CMR:\dfrac{a}{b}=\dfrac{a-c}{c-b}\)
a) \(\dfrac{a}{2}=\dfrac{b}{3};\dfrac{b}{4}=\dfrac{c}{5}\) và a+b+c=2 d) \(\dfrac{x+1}{3}=\dfrac{y-2}{4}=\dfrac{z-1}{13}\) và 2x-3y+z=42
b) 2a = 3b = 5c và a+b-c =3 i) x:y:z = 2:3:5 và x*y*z=810
c) \(\dfrac{x}{7}=\dfrac{y}{3}\) và x - 42 =y \(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\) và x2 - y2 = -16
các bạn giúp mình với, mình k biết làm. help me!!!!!
1 cho \(\dfrac{1}{c}=\dfrac{1}{2}\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\)(với a,b,c\(\ne\)0;b\(\ne\)c CMR\(\dfrac{a}{b}=\dfrac{a-c}{c-b}\)
2 cho số tự nhiên n,chứng tỏ A=\(9^{n+2}+3^{n+2}-9^n+3^n\) chia hết cho 10
với a,b,c là các số dương. CMR:
a, (a+b)(\(\dfrac{1}{a} +\dfrac{1}{b}\)) \(\ge\) 4 (1)
b, (a+b+c)(\(\dfrac{1}{a} +\dfrac{1}{b}+\dfrac{1}{c}\)) \(\ge\) 9 (2)
Cho các số dương a;b;c;d thỏa mãn:
\(a^2+c^2=1\); \(\dfrac{a^4}{b}+\dfrac{c^4}{d}=\dfrac{1}{b+d}\).
CMR \(\dfrac{a^{2006}}{b^{1003}}+\dfrac{c^{2006}}{d^{1003}}=\dfrac{2}{\left(b+d\right)^{1003}}\).
1,tìm x,y:
a)0,2 : 1\(\dfrac{1}{6}\)= \(\dfrac{2}{3}\): (6x+7)
b)\(\dfrac{a}{a+2b}\)= \(\dfrac{c}{c+2d}\). Tính \(\dfrac{a^2.d^2-4b^2.c^2}{abcd}\)
c)\(\dfrac{a}{b}\)= \(\dfrac{a^2+c^2}{ab+cd}\).CMR:\(\dfrac{a}{b}\)= \(\dfrac{c}{d}\)(b,d khác 0)
Cho a+b+c=4034 vµ \(\dfrac{1}{c+b}+\dfrac{1}{a+c}+\dfrac{1}{a+b}=\dfrac{1}{2}\) .Tính \(\dfrac{a}{c+b}+\dfrac{b}{a+c}+\dfrac{c}{a+b}\)
Bài 1:
a) Cho a(y+z) = b(z+c) = c(x+y) Tính: \(\dfrac{y-z}{a\left(b-c\right)}=\dfrac{z-c}{b\left(c-a\right)}=\dfrac{x-y}{c\left(a-b\right)}\)
b) \(Cho\dfrac{a}{2014}=\dfrac{b}{2015}=\dfrac{c}{2016}cm:4\left(a-b\right)\left(b-c\right)=\left(c-a\right)^2\)
c) \(\dfrac{a}{a'}+\dfrac{b'}{b}=1\) và \(\dfrac{b}{b'}+\dfrac{c'}{c}=1\)
cm: abc+a'b'c'=0
bài 4:
a) \(\dfrac{3x-y}{x+y}=\dfrac{3}{4}\) Tính: \(\dfrac{x}{y}\)
b) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) Tính P = \(\dfrac{xy+yz+xz}{x^2+y^2-z^2}\)
c) \(\dfrac{a}{b+c+d}=\dfrac{b}{a+c+d}=\dfrac{c}{a+b+d}=\dfrac{d}{a+b+c}\)
Tính : P = \(\dfrac{a+b}{c+d}+\dfrac{c+b}{a+d}=\dfrac{c+d}{a+b}=\dfrac{a+d}{c+b}\)
d) \(\dfrac{a+b}{c}=\dfrac{b+c}{a}=\dfrac{c+a}{b}\) Tính: \(P=\left(1+\dfrac{a}{b}\right)\left(1+\dfrac{b}{c}\right)\left(1+\dfrac{c}{a}\right)\)
Cho \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\). Tính \(A=\dfrac{bc}{a^2}+\dfrac{ca}{b^2}+\dfrac{ab}{c^2}\)
