chung minh dang thuc
-(-a+b+c)+(b+c-1)=(b-c+6)-(7-a+b)
Những câu hỏi liên quan
Chung minh bắt dang thuc a:(b+c)+b:(a+c)+c:(a+b)>=6 (a,b,c>0)
Bất đẳng thức này >=3/2!!!!!!!!!!!!!
\(\frac{a}{b+c}+1+\frac{b}{a+c}+1+\frac{c}{a+b}+1-3=\left(a+b+c\right)\cdot\left(\frac{1}{b+c}+\frac{1}{a+c}+\frac{1}{a+b}\right)\)
áp dung cosy ta có \(x+y+z\ge3\sqrt[3]{x\cdot y\cdot z}\) \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\ge3\sqrt[3]{\frac{1}{x\cdot y\cdot z}}\)
\(\Rightarrow\left(x+y+z\right)\cdot\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\ge9\Rightarrow\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\ge\frac{9}{x+y+z}\)
\(\Rightarrow\left(\frac{1}{b+c}+\frac{1}{a+c}+\frac{1}{a+b}\right)\ge\frac{9}{2\cdot\left(a+b+c\right)}\)
\(\Rightarrow\left(a+b+c\right)\cdot\left(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{a+c}\right)\ge\frac{9}{2}\)
\(\Rightarrow\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\ge\frac{9}{2}-3=\frac{3}{2}\)
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Chung minh bat dang thuc sau
B=(a+b)/c+(b+c)/a+(c+a)/b>=6 (a,b,c>0)
\(B=\left(\frac{a+b}{c}\right)+\left(\frac{b+c}{a}\right)+\left(\frac{c+a}{b}\right)\)
\(\Leftrightarrow B=\left(\frac{a}{c}+\frac{b}{c}\right)+\left(\frac{b}{a}+\frac{c}{a}\right)+\left(\frac{c}{b}+\frac{a}{b}\right)\)
\(\Leftrightarrow B=\left(\frac{a}{b}+\frac{b}{a}\right)+\left(\frac{b}{c}+\frac{c}{b}\right)+\left(\frac{a}{c}+\frac{c}{a}\right)\)
Ta cần CM BĐT : \(\frac{a}{b}+\frac{b}{a}\ge2\)
Nhân 2 vế với ab,ta đc:
\(\left(\frac{a}{b}+\frac{b}{a}\right).ab\ge2ab\Leftrightarrow\frac{a^2b}{b}+\frac{b^2a}{a}\ge2ab\Leftrightarrow a^2+b^2\ge2ab\)
\(\Leftrightarrow a^2+b^2-2ab\ge0\Leftrightarrow\left(a-b\right)^2\ge0\) (luôn đúng với mọi a,b)
=>ĐPCM
CM tương tự với 2 BĐT còn lại
Cộng theo vế các BĐT,ta đc \(B\ge2+2+2=6\)
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Giup mink cau nay nha
1,chung minh dang thuc
-(-a+b+c)+(b-c-1)=(b-c+6)-(7-a+b)+c
2,Tim x thuoc Z
(x+1)+(x+3)+(x+5)+.....+(x+99)=0
(x-3)+(x-2)+(x-1)+...+10+11=0
\(-\left(-a+b+c\right)+\left(b-c-1\right)=\left(b-c+6\right)-\left(7-a+b\right)+c\)
\(a-b-c+b-c-1=b-c+6-7+a-b+c\)
\(a-2c-1=a-1\)
\(-2c\ne0\)hay đẳng thức ko xảy ra
chung minh dang thuc:
a, - ( 49 - 3x ) + 41 = 3x - 8
b, - ( a + b + c + 1 ) + ( b - c ) - ( a - c - 1 ) = - c - 2a
a) Có VT = - (49 - 3x) + 41
= - 49 + 3x + 41 = 3x - 8 = VP (đpcm)
b) Có VT = - (a + b + c + 1) + (b - c) - (a - c - 1)
= -a - b - c - 1 + b - c - a + c + 1
= -c - 2a = VP (đpcm)
chung minh dang thuc
[a+b].[c+d]-[a+d].[b+c]=[a-c].[d-b]
(a+b)(c+d)-(a+d)(b+c)=ac+bc+ad+bd-ab-ac-cd-bd
=bc+ad-ab-cd=a(d-b)-c(d-b)=(a-c)(d-b)
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chung minh dang thuc sau;(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(c+a)
chung minh dang thuc
a, [ b+c ]-b. [ a -c]= [ a+ b].c
b, [b-c ]-a. [b+d]=a.[c+d]
chung minh dang thuc (a+b).(c+d)-(a+d).(b+c)
voi a,b,c,d la cac so duong thoa man a*b = c*d = 1. Chung minh bat dang thuc ( a+b )*( c+d ) + 4 >= 2( a+b+c+d )