Sách Toán – Học Toán – Đề Thi Toán

Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Sat, 10 Jul 2021 17:00:00 +0000 vi hourly 1 https://wordpress.org/?v=7.1.3 Đề bài: Cho tam giác $ABC$, chứng minh rằng bất đẳng thức:$2\cos C+6\cos A+3\cos B https://booktoan.com/de-bai-cho-tam-giac-abc-chung-minh-rang-bat-dang-thuc2cos-c6cos-a3cos-b.html https://booktoan.com/de-bai-cho-tam-giac-abc-chung-minh-rang-bat-dang-thuc2cos-c6cos-a3cos-b.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-tam-giac-abc-chung-minh-rang-bat-dang-thuc2cos-c6cos-a3cos-b.html 0$ ========= Chuyên mục: Bất đẳng thức […]]]> https://booktoan.com/de-bai-cho-tam-giac-abc-chung-minh-rang-bat-dang-thuc2cos-c6cos-a3cos-b.html/feed 0 Đề bài: Chứng minh rằng:$\tan^{n} A+\tan^{n} B+\tan^{n} C \geq 3 (\sqrt {3})^{n}, \forall n \geq 1 và \Delta ABC nhọn$ https://booktoan.com/de-bai-chung-minh-rangtann-atann-btann-c-geq-3-sqrt-3n-forall-n-geq-1-va-delta-abc-nhon.html https://booktoan.com/de-bai-chung-minh-rangtann-atann-btann-c-geq-3-sqrt-3n-forall-n-geq-1-va-delta-abc-nhon.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rangtann-atann-btann-c-geq-3-sqrt-3n-forall-n-geq-1-va-delta-abc-nhon.html 0$ ( […]]]> https://booktoan.com/de-bai-chung-minh-rangtann-atann-btann-c-geq-3-sqrt-3n-forall-n-geq-1-va-delta-abc-nhon.html/feed 0 Đề bài: Cho $a,b,c$ là độ dài $3$ cạnh $\triangle ABC,a\leq b\leq c$Chứng minh rằng: $\left ( a+b+c \right )^{2}\leq 9bc$ https://booktoan.com/de-bai-cho-abc-la-do-dai-3-canh-triangle-abcaleq-bleq-cchung-minh-rang-left-abc-right-2leq-9bc.html https://booktoan.com/de-bai-cho-abc-la-do-dai-3-canh-triangle-abcaleq-bleq-cchung-minh-rang-left-abc-right-2leq-9bc.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-abc-la-do-dai-3-canh-triangle-abcaleq-bleq-cchung-minh-rang-left-abc-right-2leq-9bc.html https://booktoan.com/de-bai-cho-abc-la-do-dai-3-canh-triangle-abcaleq-bleq-cchung-minh-rang-left-abc-right-2leq-9bc.html/feed 0 Đề bài: Cho $a,b,c$ là độ dài các cạnh tam giác, chứng minh: $Q=a^9b(a-b)+b^9c(b-c)+c^9a(c-a) \geq 0$ https://booktoan.com/de-bai-cho-abc-la-do-dai-cac-canh-tam-giac-chung-minh-qa9ba-bb9cb-cc9ac-a-geq-0.html https://booktoan.com/de-bai-cho-abc-la-do-dai-cac-canh-tam-giac-chung-minh-qa9ba-bb9cb-cc9ac-a-geq-0.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-abc-la-do-dai-cac-canh-tam-giac-chung-minh-qa9ba-bb9cb-cc9ac-a-geq-0.html https://booktoan.com/de-bai-cho-abc-la-do-dai-cac-canh-tam-giac-chung-minh-qa9ba-bb9cb-cc9ac-a-geq-0.html/feed 0 Đề bài: Cho $\triangle ABC$ có $r,R$ theo thứ tự là bán kính đường tròn nội tiếp và ngoại tiếp, chứng minh rằng: $\frac{r}{R}\leq \frac{1}{2}$ https://booktoan.com/de-bai-cho-triangle-abc-co-rr-theo-thu-tu-la-ban-kinh-duong-tron-noi-tiep-va-ngoai-tiep-chung-minh-rang-fracrrleq-frac12.html https://booktoan.com/de-bai-cho-triangle-abc-co-rr-theo-thu-tu-la-ban-kinh-duong-tron-noi-tiep-va-ngoai-tiep-chung-minh-rang-fracrrleq-frac12.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-triangle-abc-co-rr-theo-thu-tu-la-ban-kinh-duong-tron-noi-tiep-va-ngoai-tiep-chung-minh-rang-fracrrleq-frac12.html https://booktoan.com/de-bai-cho-triangle-abc-co-rr-theo-thu-tu-la-ban-kinh-duong-tron-noi-tiep-va-ngoai-tiep-chung-minh-rang-fracrrleq-frac12.html/feed 0 Đề bài: Chứng minh rằng nếu $a, b, c$ là độ dài ba cạnh của một tam giác có chu vi bằng $3$ thì $3{a^2} + 3{b^2} + 3{c^2} + 4abc \ge 13$ https://booktoan.com/de-bai-chung-minh-rang-neu-a-b-c-la-do-dai-ba-canh-cua-mot-tam-giac-co-chu-vi-bang-3-thi-2.html https://booktoan.com/de-bai-chung-minh-rang-neu-a-b-c-la-do-dai-ba-canh-cua-mot-tam-giac-co-chu-vi-bang-3-thi-2.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-neu-a-b-c-la-do-dai-ba-canh-cua-mot-tam-giac-co-chu-vi-bang-3-thi-2.html https://booktoan.com/de-bai-chung-minh-rang-neu-a-b-c-la-do-dai-ba-canh-cua-mot-tam-giac-co-chu-vi-bang-3-thi-2.html/feed 0 Đề bài: Gọi $a,b,c$ là độ dài các cạnh $\Delta ABC$. Tìm giá trị nhỏ nhất của biểu thức $Q=\frac{aA+bB+cC}{a+b+c}$ https://booktoan.com/de-bai-goi-abc-la-do-dai-cac-canh-delta-abc-tim-gia-tri-nho-nhat-cua-bieu-thuc.html https://booktoan.com/de-bai-goi-abc-la-do-dai-cac-canh-delta-abc-tim-gia-tri-nho-nhat-cua-bieu-thuc.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-goi-abc-la-do-dai-cac-canh-delta-abc-tim-gia-tri-nho-nhat-cua-bieu-thuc.html https://booktoan.com/de-bai-goi-abc-la-do-dai-cac-canh-delta-abc-tim-gia-tri-nho-nhat-cua-bieu-thuc.html/feed 0 Đề bài: Chứng minh rằng trong mọi tam giác $ABC$ nhọn ta đều có: $\frac{2}{3}(\sin A+\sin B+\sin C)+\frac{1}{3}(\tan A+\tan B+\tan C)> \pi$. https://booktoan.com/de-bai-chung-minh-rang-trong-moi-tam-giac-abc-nhon-ta-deu-co-frac23sin-asin-bsin-cfrac13tan-at.html https://booktoan.com/de-bai-chung-minh-rang-trong-moi-tam-giac-abc-nhon-ta-deu-co-frac23sin-asin-bsin-cfrac13tan-at.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-trong-moi-tam-giac-abc-nhon-ta-deu-co-frac23sin-asin-bsin-cfrac13tan-at.html \pi$. Lời giải Đề bài: Chứng minh rằng trong mọi tam giác $ABC$ nhọn ta đều có: $\frac{2}{3}(\sin A+\sin B+\sin C)+\frac{1}{3}(\tan A+\tan B+\tan C)> \pi$. Lời giải Xét hàm số : $f(x)=\frac{2}{3}\sin x+\frac{1}{3}\tan x-x$ […]]]> https://booktoan.com/de-bai-chung-minh-rang-trong-moi-tam-giac-abc-nhon-ta-deu-co-frac23sin-asin-bsin-cfrac13tan-at.html/feed 0 Đề bài: 1) Cho tam giác $ABC$ thỏa mãn điều kiện: $max ({h_a},{h_b},{h_c}) < 1$Chứng minh rằng: khi đó ta có $S < \frac{{\sqrt 3 }}{3}$2) Cho tam giác $ABC$ thỏa mãn điều kiện : ${l_a} + {l_b} + {l_c} = \frac{{a + b + c}}{3}(\frac{{ab}}{{a + b}} + \frac{{bc}}{{b + c}} + \frac{{ac}}{{a + c}})$Chứng minh rằng: $R \ge 1$ https://booktoan.com/de-bai-1-cho-tam-giac-abc-thoa-man-dieu-kien-max-h_ah_bh_c-1chung-minh-rang-khi-do-ta-co-s-fracsqrt-3-32-cho-tam-giac-abc-thoa-man-d.html https://booktoan.com/de-bai-1-cho-tam-giac-abc-thoa-man-dieu-kien-max-h_ah_bh_c-1chung-minh-rang-khi-do-ta-co-s-fracsqrt-3-32-cho-tam-giac-abc-thoa-man-d.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-1-cho-tam-giac-abc-thoa-man-dieu-kien-max-h_ah_bh_c-1chung-minh-rang-khi-do-ta-co-s-fracsqrt-3-32-cho-tam-giac-abc-thoa-man-d.html https://booktoan.com/de-bai-1-cho-tam-giac-abc-thoa-man-dieu-kien-max-h_ah_bh_c-1chung-minh-rang-khi-do-ta-co-s-fracsqrt-3-32-cho-tam-giac-abc-thoa-man-d.html/feed 0 Đề bài: Cho: $\triangle ABC$ và $x,y,z>0$.Chứng minh rằng:$\frac{1}{x}\cos A+\frac{1}{y}\cos B+\frac{1}{z}\cos C\leq \frac{x^{2}+y^{2}+z^{2}}{2xyz}$ https://booktoan.com/de-bai-cho-triangle-abc-va-xyz0-chung-minh-rangfrac1xcos-afrac1ycos-bfrac1zcos-cleq-fracx2y2z22xyz.html https://booktoan.com/de-bai-cho-triangle-abc-va-xyz0-chung-minh-rangfrac1xcos-afrac1ycos-bfrac1zcos-cleq-fracx2y2z22xyz.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-triangle-abc-va-xyz0-chung-minh-rangfrac1xcos-afrac1ycos-bfrac1zcos-cleq-fracx2y2z22xyz.html 0$.Chứng minh rằng:$\frac{1}{x}\cos A+\frac{1}{y}\cos B+\frac{1}{z}\cos C\leq \frac{x^{2}+y^{2}+z^{2}}{2xyz}$ Lời giải Đề bài: Cho: $\triangle ABC$ và $x,y,z>0$.Chứng minh rằng:$\frac{1}{x}\cos A+\frac{1}{y}\cos B+\frac{1}{z}\cos C\leq \frac{x^{2}+y^{2}+z^{2}}{2xyz}$ Lời giải Gọi O là tâm đường tròn nội tiếp $\triangle ABC$.Ta có: $(x.\overrightarrow {OM}+y.\overrightarrow {ON}+z.\overrightarrow {OP})^{2}\geq 0 (1)$Khai triển $(1)$ ta có:$(x^{2}+y^{2}+z^{2}).r^{2}+2(xy.\overrightarrow {OM}.\overrightarrow {ON}+yz.\overrightarrow {ON}.\overrightarrow {OP}+zx.\overrightarrow […]]]> https://booktoan.com/de-bai-cho-triangle-abc-va-xyz0-chung-minh-rangfrac1xcos-afrac1ycos-bfrac1zcos-cleq-fracx2y2z22xyz.html/feed 0