cho hai so huu ti a/b va c/d voi mau duong, trong do a/b < c/d . chung minh rang :
a . ad < bc b . a/b < a+c / b+d < c/d
giup mk nha
Cho hai so huu ti a/b va c/d (b>0, d>0). Chung to rang :
a, Neu a/b < c/d thi ad<cd
b, Neu ad<bc thi a/b < c/d
cho so huu ti a/b va c/d voi b>0 chung to rang neu a/b > c/d thì a/b<a+c/b+d <c/d
C1 : Theo ví dụ trên ta có : \(\frac{a}{b}< \frac{c}{d}\)=> ad < bc
Suy ra :
<=> ad + ab < bc + ba <=> a[b + d] < b[a + c] <=> \(\frac{a}{b}< \frac{a+c}{b+d}\)
Mặt khác ad < bc => ad + cd < bc + cd
<=> d[a + c] < [b + d]c <=> \(\frac{a+c}{b+d}< \frac{c}{d}\)
Từ đó suy ra \(\frac{a}{b}< \frac{a+c}{b+c}< \frac{c}{d}\)
C2 : Xét hiệu : \(\frac{a+c}{b+d}-\frac{a}{b}=\frac{ab+bc-ab-ad}{b(b+d)}=\frac{bc-ad}{b(b+d)}>0\)
\(\frac{c}{d}-\frac{a+c}{b+d}=\frac{bc+cd-ad-cd}{d(b+d)}=\frac{bc-ad}{d(b+d)}>0\)
Cau 1: Cho tam giac ABC cuong tai A, AB=8cm; AC=15cm. Ve duong cao AH
a) chung minh AB^2= BH. BC
b) Tinh BH, CH, AH, BC
c) Ve phan giac AD cua tam giac ABC. Chung minh H nam giua B va D
d) Tinh ti so dien tich D HAC va D A.BC
Cau 2: Cho tam giac ABC vuong tai A, AB=5cm; Ac=12cm, ve duong cao AH va duong phan giac AD.
a) Tinh BC, BD
b) Chung minh D ACH: D ABC; tinh AH
c) Qua B ke duong thang vuong goc voi AB cat tia AD tai K. Chung minh AB.AD =AC. KD
.Cau 3: Cho tam giac ABC vuong A co AB = 5cm; AC=12cm. Ve dcao AH va pgiac AD cua goc BAC
a) Tih BC; BD
b) Chung minh D HAC : D ABC
c) Qua B ke duong vgoc voi BA cat AD tai k. Chung minh AB.AD= AC.KD
cho so huu ti a/b voi a,b thuoc Z, b>0. Chung minh rang: neu co a<b va >0 thi a/b<a+c/b+c
Ta có a<b
=>ac<bc (c>0)
=> ac+ ab < bc+ ab
=> a(b+c) < b(a+c)
=> a/b< a+c/b+c(đpc/m)
a)Chung to rang neu a/b <c/d (b<0,d<0) thi a/b < a+c/d+b < c/d
b)Hay viet 3 so huu ti xen giua -1/3 va -1/4
\(\frac{a}{b}< \frac{c}{d}\) => ad < bc
=> ad + ab < bc + ab
=> a(b + d) < b(a + c)
=> \(\frac{a}{b}< \frac{a+c}{b+d}\)
=> ad < bc
=> ad + cd< bc + cd
=> d(a + c) < c(b + d)
=> \(\frac{a+c}{b+d}< \frac{c}{d}\)
=> đccm
b) \(\frac{-1}{3}=\frac{-16}{48}< \frac{-15}{48}\); \(\frac{-14}{48};\frac{-13}{48}\)\(< \frac{-12}{48}=\frac{-1}{4}\)
ok mk nhé!!! 4556577568797902451353466545475678769863513532345634645645745
tren duong thang xy cho truoc lay 4 diem theo thu tu A,B,C,D biet AB=2cm,BC=5cm,AD=9cm
a,Tinh AC
b,Tinh CD
c, so sanh do dai doan AC voi doan BC
d, chung to rang trung diem cua AD trung voi trung diem doan BC
CHO TAM GIAC ABC VUONG TAI A, DUONG CAO AH.TREN CANH BC LAY DIEM D SAO CHO BD=BA.DUONG VUONG GOC VOI BC TAI D CAT AC O E
A) SO SANH AE VA DE
B) CHUNG MINH TIA AD LA PHAN GIAC CUA GOC HAC
C) VE DK VUONG GOC VOIAC TAI K. CHUNG MINH RANG AK=AH
D) CHUNG MINH RANG AB+AC<BC+AH
cho hinh chu nhat ABCD co AD= 6cm, AB=8cm, hai duong cheo AC va BD cat nhau tai O. Qua D ke duong thang d vuong goc voi BD, d cat BC tai E.
a) Chung Minh: Tam giac BDC dong dang voi tam giac DCE.
b) Ke CH vuong goc voi DE tai H. CMR: DC.DC=CH.DB
c) goi K la giao diem cua OE va HC. Chung minh K la Trung diem cua HC va tinh ti so dien tich tam giac EHC vatam giac EDB.
d) Chung Minh Rang: Ba duong thang OE, CD, BH Dong Quy.
( Ve Hinh Nhe)
Cho 4 so nguyen duong a,b,c,d ma trong do b la trung binh cong cua 2 so a va c.Chung minh rang 4 so a,b,c,d lap thanh mot ti le thuc neu \(\frac{2}{c}\)=\(\frac{1}{b}+\frac{1}{d}\)
Ta có : \(b=\frac{a+c}{2}\) \(\implies\) \(2b=a+c\)
\(\frac{2}{c}=\frac{1}{b}+\frac{1}{d}\)
\(\implies\) \(\frac{1}{2}.\frac{2}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)
\(\implies\) \(\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)
\(\iff\) \(\frac{1}{c}=\frac{b+d}{2db}\)
\(2db=c.\left(b+d\right)\)
\(\left(a+c\right)d=cd+cb\)
\(ad+cd=cd+cb\)
\(ad=cb\)
\(\frac{a}{c}=\frac{b}{d}\) là một tỉ lệ thức \(\left(đpcm\right)\)