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 \(\left(đpcm\right)\)
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
Viet bieu thuc dai so bieu thi:
a) tich cua 3 so nguyen lien tiep;
b) tong cac binh phuong cua 2 so le bat ki
c) thuong cua 2 so nguyen trong do mot so chia cho 3 du 1 ,mot so chia cho 3 du 2;
d) luy thua bac n cua tong hai so a va b
cho a, b, c, d la 4 so nguyen duong thoa man: b= \(\frac{a+c}{2}va\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)
chung minh: \(\frac{a}{b}=\frac{c}{d}\)
cho a+d=b+c va a2+d2=b2+c2 (b,d khac 0). cm 4 so a,b,c,d co the lap thanh 1 ti le thuc
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=
cho x,y,z la cac so nguyen duong va x+y+z la so le, cac so thuc a,b,c thoa man (a-b)/x=(b-c)/y=(a-c)/z. chung minh rang a=b=c
cho a+b/a-b=c+a/c-a va abc khac 0 chung minh rang tu 3 so abc ( co 1 so su dung 2 lan co the lap thanh 1 ti le thuc
1) Tinh dien tich manh dat hinh chu nhat biet rang ti so giua hai canh cua no = \(\frac{4}{5}\)va chu vi = 108m. 2) Biet rang \(a^2=b.c\)voi \(a\ne b,a\ne c\)Chung minh: \(\frac{a+b}{a-b}=\frac{c+a}{c-a}\) 3) Tim so hoc sinh cua hai lop 7A va 7B, biet rang so HS lop 7A it hon lop 7B la 5 em va ti so cua hai lop la 8:9 4) Chung minh: Neu \(\frac{a}{b}=\frac{c}{d}\)thi \(\frac{a+b}{b}=\frac{c+d}{d}\left(a,b,c\ne0\right)\)
a. Xac dinh a de nghiem cua da thuc f(x) = 2x-4 cung la nghiem cua da thuc g(x) = x^2 - ax +2b.
b. Cho f(x) = ax^3 + bx^2 + cx + d, trong do a; b; c; d la hang so va thoa man : b = 3a + c
Chung to rang : f(1) = f(-2)
