Cho ba don thuc:\(M=-5xy\),\(N=11xy^2\),\(P=\frac{7}{5}x^2y^3\).Chung minh rang ba don thuc nay khong the cung co gia tri duong.
Cho tam giac ABC vuong can tai A, M la trung diem cua BCBC. Lay diem D bat ki thuoc doan BM ( D \(\ne\)B, D\(\ne\)M ). H va I thu tu la hinh chieu cua B, C xuong duong thang AD. Duong thang AM cat CI tai N. Chung minh rang:
a) BH = AI.
b) BH^2 + CI^2 co gia tri khong doi.
c) IM la tia phan giac cua goc HIC.
Cho hai đa thức N = 5 x 2 - 3 x y , M = 5 x y + 2 x 2 - 2 y 2 . Tìm đa thức P biết P + N = M
A. - 3 x 2 + 8 x y - 2 y 2
B. 7 x 2 + 2 x y - 2 y 2
C. - 3 x 2 - 8 x y + 2 y 2
D. - x 2 + 8 x y + 2 y 2
cho 9 duong thang trong do khong co 2 duong thang nao song song chung minh rang it nhat cung co 2 duong thang ma goc nhon giua chung khong nho hon 20 do
cho 3 duong thang phan biet a,b,c.Biet rang a va b cung song song voi c.Mot duong thang d khong song song voi a.Chung minh rang d cat b va c.Cac duong thang a,b co cat nhau khong?
cho 9 duong thang trong do khong co 2 duong thang nao song song . chung minh rang it nhat cung co 2 duong thang magoc nhon giua chung ko nho hon 20
bai 1 tim cac stn x y z sao cho x+y+z=xyz
bai 2cmr neu m^2+mn+n^2chia het cho 9 voi m ,n la cac stn thi m,n chia het cho 3
bai 3 tim stn n nho nhat de cac phan so sau toi gian
7/n+9.8/n+10,...,31/n+33
bai 4chung to rang phan so m^3+2m/m^4+3m^2 +1 toi gian
bai 5 a,cmr khong ton tai so chinh phuong nao co dang abab
b,cho 51 so nguyen duong khong vuot qua 100 cmr ton tai 2 so trong 51 so noi tren ma 1 so chia het cho so con lai
c,tim cac so co 3 chu so sao cho hieu cua so ay va gom 3 chu so ay viet theo thu tu nguoc lai la mot so chinh phuong
bai 6cmr A=2x(x+y-1)+y^2+1 luon nhan gia tri khong am voi moi x,y
bai 7 tim hai so nguyen duong sao cho tong ,hieu thuong (so lon chia cho so nho )cua chung cong lai duoc 38
bai 8 cho ba so a,b,c thoa man a/2009=b/2010=c/2011
tinh gia tri cua bieu thuc M=4(a-b)(b-c)-(c-a)^2
Chung minh rang ba don thuc khong cung gia tri am
Cho duong thang xy di qua diem O. Ve tia Oz sao cho xÔz bang 135 do . Tren nua mat phang bo xy khong chua tia Oz ve tia Ot sao cho yÔt bang 90 do. Goi Ov la tia phan giac cua xÔt
A) Chung to rang Oz va Ov la hai tia doi nhau.
B) Cac goc xÔv va yÔz co phai la hai goc doi dinh khong. Vi sao