CMR:Voi 3 so a,b,c duong thi
a) (a+b)(1/a+1/b)>/4
b) (a+b+c)(1/a+1/b+1/c)>/9
c) 2a/bc+b+c/2a>/2
giup mk giai bai nay vs cac ban
DUNG MK SE TICH CHO
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giup mk bai nay voi :
A = ( -2a +3b -4c ) - (-2a - 3b -4c )
a, Rut gon
b, tinh gia tri cua A khi a = 2012 ; b= -1 ; c= -2013
ai nhanh mk se cho 1 like
\(A=\left(-2a+3b-4c\right)-\left(-2a-3b-4c\right)\)
\(a,=-2a+3b-4c+2a+3b+4c\)
\(=\left(-2a+2a\right)+\left(3b+3b\right)+\left(-4c+4c\right)\)
\(=0+\left(3b+3b\right)+0\)
\(=3b+3b=2.3b\)
\(b,\)Thay \(a=2012;b=-1;c=-2013\)vào biểu thức \(A\) ta có \(:\)
\(A=\left[-2.2012+3.\left(-1\right)-4.\left(-2013\right)\right]\)\(-\left[-2.\left(2012\right)-3.\left(-1\right)-4.\left(-2013\right)\right]\)
\(A=0\)
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1 Tim a biet .
a+b-c=18. voi b=10;c=-9
2a-3b+c=0
1-2b+c-3a=-9. voi b=-3 ;c=-7
Cac ban giup minh giai bai nay nhe cam on nhieu...
cho cac so a,b,c duong thoa man ab+bc+ca=1 chung minh : \(p=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\)
Cho cac so nguyen duong a,b,c,x,y,z1, Biet 1/a 3/b + c 5/c + a. Hay rut gon phan so A a/2b - c2. Biet a/b 2b/cc 4c/a. Hay rut gon phan so B ab + bc + ca/a2 + b + c23. Biet x/a y/b z/c. Hay rut gon phan so C x*y*z*(b+c)*(c+a)*(a+b)/a*b*c(y+z)*(z+x)*(x+y)4. Biet ab/a + 2b 2/5; bc/b + 2c 3/4; ca/c +2a 3/5. Hay rut gon phan so D abc/ab+bc+ca5. Biet 3/a -4b 5c. Hay rut gon phan so E 3bc + ab - 4ac/6bc - 8ac -abGiup minh nhe! Ai lam duoc va dung cho tick.Thanks cac ban
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Cho cac so nguyen duong a,b,c,x,y,z
1, Biet 1/a = 3/b + c = 5/c + a. Hay rut gon phan so A = a/2b - c
2. Biet a/b = 2b/cc = 4c/a. Hay rut gon phan so B = ab + bc + ca/a2 + b + c2
3. Biet x/a = y/b =z/c. Hay rut gon phan so C = x*y*z*(b+c)*(c+a)*(a+b)/a*b*c(y+z)*(z+x)*(x+y)
4. Biet ab/a + 2b = 2/5; bc/b + 2c = 3/4; ca/c +2a = 3/5. Hay rut gon phan so D = abc/ab+bc+ca
5. Biet 3/a -4b = 5c. Hay rut gon phan so E = 3bc + ab - 4ac/6bc - 8ac -ab
Giup minh nhe! Ai lam duoc va dung cho tick.
Thanks cac ban
xin lỗi tớ ấn nhầm chỗ M=7 tớ làm lại rồi đó
ban tra loi het cac cau hoi phia tren kia ho minh dc ko?
Cho cac so nguyen duong a,b,c,x,y,z1, Biet 1/a 3/b + c 5/c + a. Hay rut gon phan so A a/2b - c2. Biet a/b 2b/cc 4c/a. Hay rut gon phan so B ab + bc + ca/a2 + b + c23. Biet x/a y/b z/c. Hay rut gon phan so C x*y*z*(b+c)*(c+a)*(a+b)/a*b*c(y+z)*(z+x)*(x+y)4. Biet ab/a + 2b 2/5; bc/b + 2c 3/4; ca/c +2a 3/5. Hay rut gon phan so D abc/ab+bc+ca5. Biet 3/a -4b 5c. Hay rut gon phan so E 3bc + ab - 4ac/6bc - 8ac -abGiup minh nhe! Ai lam duoc va dung cho tick.Thanks cac ban
Đọc tiếp
Cho cac so nguyen duong a,b,c,x,y,z
1, Biet 1/a = 3/b + c = 5/c + a. Hay rut gon phan so A = a/2b - c
2. Biet a/b = 2b/cc = 4c/a. Hay rut gon phan so B = ab + bc + ca/a2 + b + c2
3. Biet x/a = y/b =z/c. Hay rut gon phan so C = x*y*z*(b+c)*(c+a)*(a+b)/a*b*c(y+z)*(z+x)*(x+y)
4. Biet ab/a + 2b = 2/5; bc/b + 2c = 3/4; ca/c +2a = 3/5. Hay rut gon phan so D = abc/ab+bc+ca
5. Biet 3/a -4b = 5c. Hay rut gon phan so E = 3bc + ab - 4ac/6bc - 8ac -ab
Giup minh nhe! Ai lam duoc va dung cho tick.
Thanks cac ban
cho 3 so thuc duong a, b, c thoa man 1/a+1/c=2/b. tim GTNN cua (a+b)/(2a-b)+(b+c)(/2c-b)
\(\frac{1}{a}+\frac{1}{c}=\frac{2}{b}\Leftrightarrow b=\frac{2ac}{a+c}\)
\(P=\frac{a+b}{2a-b}+\frac{b+c}{2c-b}=\frac{a+\frac{2ac}{a+c}}{2a-\frac{2ac}{a+c}}+\frac{\frac{2ac}{a+c}+c}{2c-\frac{2ac}{a+c}}=\frac{a+3c}{2a}+\frac{3a+c}{2c}=1+\frac{3}{2}\left(\frac{a}{c}+\frac{c}{a}\right)\ge4\)
Dấu "=" xảy ra khi \(a=b=c\)
cac bn giup mk bai nay vs !ai nhanh mk se tick
(3^A-1)(3^A-2)(3^A-3)(3^A-4)(3^A-5)(3^A-6)=2019^b+20159
A=5/9 - 7/8 + 2/3 + 4/9 - 1/8 + 1/3
B= 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
a) Tính A và B
b) Tìm C bíêt ( A - 7B) cua C bang 2010
Cau A và B mk dã giai roi , cau A ra 1, B ra 6/7 ,cac bn chi can giup mk cau C thoi , cauC mk ko bt cach giai!!!
Bn nao giup mk , mk se tick.
giúp mk câu ni vs::cho các số dương a,b,c thõa mãn ab+bc+ac=1. Tìm giá trị lớn nhất của biểu thức P= 2a/căn(1+a^2) +b/căn(1+b^2)+c/căn(1+c^2)
Áp dụng BĐT Cauchy-Schwarz ta có:
\(P=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\)
\(=\frac{2a}{\sqrt{\left(a+b\right)\left(a+c\right)}}+\frac{b}{\sqrt{\left(a+b\right)\left(b+c\right)}}+\frac{c}{\sqrt{\left(a+c\right)\left(b+c\right)}}\)
\(=\sqrt{\frac{2a}{a+b}\cdot\frac{2a}{a+c}}+\sqrt{\frac{2b}{a+b}\cdot\frac{b}{2\left(b+c\right)}}+\sqrt{\frac{2c}{a+c}\cdot\frac{c}{2\left(b+c\right)}}\)
\(\le\frac{1}{2}\left(\frac{2a}{a+b}+\frac{2b}{a+b}+\frac{2a}{a+c}+\frac{2c}{a+c}+\frac{b}{2\left(b+c\right)}+\frac{c}{2\left(b+c\right)}\right)\)
\(=\frac{1}{2}\left(2+2+\frac{1}{2}\right)=\frac{9}{4}\)
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Áp dụng BĐT Cauchy-Schwarz ta có :
\(P=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\)
\(=\frac{2a}{\sqrt{\left(a+b\right)\left(a+c\right)}}+\frac{b}{\sqrt{\left(a+b\right)\left(b+c\right)}}+\frac{c}{\sqrt{\left(a+c\right)\left(b+c\right)}}\)
\(=\sqrt{\frac{2a}{a+b}.\frac{2a}{a+c}}+\sqrt{\frac{2b}{a+b}.\frac{b}{2\left(b+c\right)}}+\sqrt{\frac{2c}{a+c}.\frac{c}{2\left(b +c\right)}}\)
\(\le\frac{1}{2}\left(\frac{2a}{a+b}+\frac{2b}{a+b}+\frac{2a}{a+c}+\frac{2c}{a+c}+\frac{b}{2\left(b+c\right)}+\frac{c}{2\left(b+c\right)}\right)\)
\(=\frac{1}{2}\left(2+2+\frac{1}{2}\right)=\frac{9}{4}\)
P/s : Mình tự nghĩ chứ không phải mình copy đâu
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