chung minh rang voi moi n lon hon 1 ta co \(\sqrt{2\sqrt{3\sqrt{4...\sqrt{\left(n-1\right)\sqrt{n}}}}}< 3\)
CMR voi moi so nguyen n\(\ge\)2 thi \(\sqrt[n]{2}\) la so vo ti
giai ho minh bai nay voi
cho a,b,c la do dai 3 canh tam giac va an;bn;cn cung la do dai 3 canh tam giac voi n la so nguyen duong. Chung minh rang 2 trong 3 so a,b,c bang nhau
cho n la mot so chinh phuong bat ki . CMR n co dang 4k hoac 4k +1 voi k la so tu nhien
giúp toi lam bai nay voi tri tuyet doi cua X1 - X2 lon hon hoac bang 2
Vi-et S= X1 +X2 = M +1
P= X1.X2 = M
Tìm một sô co 2 chu so biết rang tong 2 so bang 8 . Nếu đoi cho cho nhau ta được 1 so lon hon so ban đau la 18 đon vi
Cho 2 duong tron (O;R) va (O';R') tiep xuc ngoai tai A (R > R'). Ve day AM cua duong tron (O) va day AN cua duong tron (O') sao cho AM vuong goc AN. Goi BC la mot tiep tuyen chung ngoai cua 2 duong tron (O) va(O') voi B thuoc (O) va C thuoc (O').
a) CMR 3 duong thang MN, BC va OO' dong quy.
b) Xac dinh vi tri cua M va N de tu giac MNOO' co dien tich lon nhat. Tinh gia tri lon nhat do.
Cho 3 so duong thoa man\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\) . Chung minh rang \(\sqrt{x+yz}+\sqrt{y+zx}+\sqrt{z+xy}\)lon hon hoac bang\(\sqrt{xyz}+\sqrt{x}+\sqrt{y}+\sqrt{z}\)
cho a+b+\(\frac{1^{ }}{a^2}+\frac{1}{b^2}\)lon hon hoac bang 9
