Cho cac so huu ti x=\(\frac{a}{b}\), y =\(\frac{c}{d}\)b>0,d>0 va cac so tu nhien m,n voi m ,n khac 0 CMR
\(\frac{a}{b}< \frac{c}{d}\) thi \(\frac{a}{b}< \frac{ma+nc}{mb+nd}< \frac{c}{d}\)
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cau 1: Cho A frac{100^{2014}+2}{3}-frac{100^{2015}+17}{9}.tong cac cua so cua B-9ACau 2: So sanh Afrac{1}{1.2}+frac{1}{2.3}+frac{1}{3.4}+........+frac{1}{100.101}voi 1 ta doc A....1Cau 3 : Cho bon so a,b,c,d sao cho a+b+c+d khac 0 . Biet frac{b+c+d}{a}frac{c+d+a}{b}frac{d+a+b}{c}frac{a+b+c}{d}k. Vay kCau 4 : so cac so nguyen am x thoa man x^{2015}left(-2right)^{2014}Cau 5; tim x,y,z biet frac{x}{y}frac{10}{9},frac{y}{z}frac{3}{4}va x-y+z78Cau 6: tap hop cac so co ba chu so chia het cho 18 va to...
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cau 1: Cho A= \(\frac{100^{2014}+2}{3}-\frac{100^{2015}+17}{9}.\)tong cac cua so cua B=-9A
Cau 2: So sanh A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+........+\frac{1}{100.101}\)voi 1 ta doc A....1
Cau 3 : Cho bon so a,b,c,d sao cho a+b+c+d khac 0 . Biet \(\frac{b+c+d}{a}=\frac{c+d+a}{b}=\frac{d+a+b}{c}=\frac{a+b+c}{d}=k\). Vay k=
Cau 4 : so cac so nguyen am x thoa man \(x^{2015}=\left(-2\right)^{2014}\)
Cau 5; tim x,y,z biet \(\frac{x}{y}=\frac{10}{9},\frac{y}{z}=\frac{3}{4}\)va x-y+z=78
Cau 6: tap hop cac so co ba chu so chia het cho 18 va tong cac chu so ti le voi 1;2;3 la
Cau 7: gia tri cua tong S=1.2+2.3+.....+49.50 la S=
So sanh A=\(\frac{2015}{2015^m}+\frac{2015}{2015^n}\)va B=\(\frac{2013}{2015^m}+\frac{2017}{2015^n}\) [m,n la cac so tu nhien khac 0]
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\(B=\frac{215-2}{2015^m}+\frac{2015+2}{2015^n}=\frac{2015}{2015^m}-\frac{2}{2015^m}+\frac{2015}{2015^n}+\frac{2}{2015^n}=A-2\left(\frac{1}{2015^m}-\frac{1}{2015^n}\right)\)
+ Nếu \(m>n\Rightarrow2015^m>2015^n\Rightarrow\frac{2}{2015^m}<\frac{2}{2015^n}\Rightarrow\frac{2}{2015^m}-\frac{2}{2015^n}<0\Rightarrow A-\left(\frac{2}{2015^m}-\frac{2}{2015^n}\right)>A\)
=> A<B
+ Nếu
m<n làm tương tự => A>B
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Cho hai so huu ti \(\frac{a}{b}\)va\(\frac{c}{d}\)(b>0, d>0)
Chung minh:\(\frac{a}{b}\)< \(\frac{c}{d}\)
cho \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\) voi a; b; c khac 0 va c khac cong tru d . CMR \(\frac{a}{b}=\frac{c}{d}\)
co ai biet ko? Neu biet thi giup mk voi
Câu 13 Tập hợp tất cả các giá trị của x thỏa mãn x^3-1laf :
A . ( 0;-1) B .(0) C.∅ D.(0;-1;1)
Câu 15: Cho ABC có MN //BC thì:
A.frac{AM}{NC}frac{MB}{AN} B.frac{AN}{MB}frac{AM}{NC} C.frac{AM}{MB}frac{AM}{NC} D.frac{MB}{MA}frac{NA}{NC}
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Câu 13 Tập hợp tất cả các giá trị của x thỏa mãn \(x^3=-1\)laf :
A . ( 0;-1) B .(0) C.∅ D.(0;-1;1)
Câu 15: Cho ABC có MN //BC thì:
A.\(\frac{AM}{NC}\)=\(\frac{MB}{AN}\) B.\(\frac{AN}{MB}=\frac{AM}{NC}\) C.\(\frac{AM}{MB}=\frac{AM}{NC}\) D.\(\frac{MB}{MA}=\frac{NA}{NC}\)
cho ti le thuc \(\frac{a}{b}\)=\(\frac{c}{d}\)
chung minh rang\(\frac{a}{b}\)=\(\frac{7a+5c}{7b+5d}\)[b+d khac 0]
cac ban co biet tai sao minh go dau cac chu cai thi chu cai do va dau deu bien mat khong? giup minh voi , cau hoi tren la 1 vi du
Giai va bien luan cac phuong trinh sau:
1. \(\frac{a+b-x}{c}+\frac{a+c-x}{b}+\frac{b+c-x}{a}+\frac{4x}{a+b+c}=1\)
(an x) voi dk; a,b,b khac 0 va a+b+c khac 0
2.\(\frac{x-a}{bc}+\frac{x-b}{ac}+\frac{x-c}{ab}=2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
(an x) voi dk: a,b,c khac 0
3, \(\frac{mx+3}{6}+\frac{m^2-1}{2}=\frac{x+5}{10}+\frac{2}{5}\left(x+m^2+1\right)\)
(an x)
tim tat ca cac so tu nhien a, b, c khac 0 va khac nhau sao cho:
\(\frac{1}{a}\) +\(\frac{1}{b}\) +\(\frac{1}{c}\) =1
ta có: a,b,c thuộc n nên;
1:a+1:b+1:c=1
1:(a+b+c)=1
a+b+c=1vìa, b, cthuoocj N, nên a=0 thìb=0vafc=1
hoặc a=1 thì bvafc=0
hoăcj
b=1 thì a,c=0
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Cau 1; chofrac{x}{2}frac{y}{5}vaxy90. So cap (x;y) thoa man laCau 2 : Cho a+db+c va a^2+d^2b^2+c^2(b,d khac 0).Khi do 4 so lap thanh ti le thuc naoCau 3 :GTLN cua phan so frac{7n-8}{2n-3}Cau 4: Cho Afrac{12}{x-15} dieu kien de 0A1 va A1Cau 5 ; tim x biet /-x-5//x510Cau 6: tap hop cac so nguyen cua x thoa man (3x^2-51)^2014(-24)^2014Cau 7: tap hop cac so thoa man /x-y/+/y+9/25/0
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Cau 1; cho\(\frac{x}{2}=\frac{y}{5}\)vaxy=90. So cap (x;y) thoa man la
Cau 2 : Cho a+d=b+c va \(a^2+d^2=b^2+c^2\)(b,d khac 0).Khi do 4 so lap thanh ti le thuc nao
Cau 3 :GTLN cua phan so \(\frac{7n-8}{2n-3}\)
Cau 4: Cho A=\(\frac{12}{x-15}\) dieu kien de 0<A<1 va A>1
Cau 5 ; tim x biet /-x-5//x=5=10
Cau 6: tap hop cac so nguyen cua x thoa man (3x^2-51)^2014=(-24)^2014
Cau 7: tap hop cac so thoa man /x-y/+/y+9/25/=0
