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=7.1.2 Đề bài: Chứng minh rằng: $\sqrt{a^{2}+b^{2}}+\sqrt{c^{2}+d^{2}}\geq \sqrt{(a+c)^{2}+(b+d)^{2}}$ (1) https://booktoan.com/de-bai-chung-minh-rang-sqrta2b2sqrtc2d2geq-sqrtac2bd2-1.html https://booktoan.com/de-bai-chung-minh-rang-sqrta2b2sqrtc2d2geq-sqrtac2bd2-1.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-sqrta2b2sqrtc2d2geq-sqrtac2bd2-1.html https://booktoan.com/de-bai-chung-minh-rang-sqrta2b2sqrtc2d2geq-sqrtac2bd2-1.html/feed 0 Đề bài: Cho $a+b+c=6 (1)$Hãy chứng minh $a^2+b^2+c^2 \geq 12 (2)$ https://booktoan.com/de-bai-cho-abc6.html https://booktoan.com/de-bai-cho-abc6.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-abc6.html https://booktoan.com/de-bai-cho-abc6.html/feed 0 Đề bài: Chứng minh rằng:$C_{n}^{0}-\frac{1}{3}C_{n}^{1}+\frac{1}{5}C_{n}^{2}+…+\frac{(-1)^{n}}{2n+1}C_{n}^{n}\geq \sqrt{\frac{3n+1}{4n^{2}+4n+1}}$ https://booktoan.com/de-bai-chung-minh-rangc_n0-frac13c_n1frac15c_n2-frac-1n2n1c_nngeq-sqrtfrac3n14n24n1.html https://booktoan.com/de-bai-chung-minh-rangc_n0-frac13c_n1frac15c_n2-frac-1n2n1c_nngeq-sqrtfrac3n14n24n1.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rangc_n0-frac13c_n1frac15c_n2-frac-1n2n1c_nngeq-sqrtfrac3n14n24n1.html https://booktoan.com/de-bai-chung-minh-rangc_n0-frac13c_n1frac15c_n2-frac-1n2n1c_nngeq-sqrtfrac3n14n24n1.html/feed 0 Đề bài: Cho ba số $a,b,c$ thoả mãn: $\begin{cases}a+b+c=2 \\ a^2+b^2+c^2=2 \end{cases}$.Chứng minh rằng $0\leq a,b,c\leq \frac{4}{3}$. https://booktoan.com/de-bai-cho-ba-so-abc-thoa-man-begincasesabc2-a2b2c22-endcases-chung-minh-rang-0leq-abcleq-frac43.html https://booktoan.com/de-bai-cho-ba-so-abc-thoa-man-begincasesabc2-a2b2c22-endcases-chung-minh-rang-0leq-abcleq-frac43.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-ba-so-abc-thoa-man-begincasesabc2-a2b2c22-endcases-chung-minh-rang-0leq-abcleq-frac43.html https://booktoan.com/de-bai-cho-ba-so-abc-thoa-man-begincasesabc2-a2b2c22-endcases-chung-minh-rang-0leq-abcleq-frac43.html/feed 0 Đề bài: Cho $x+2y+3z=2$.Chứng minh rằng:$\sqrt{1+x^{2}}+2\sqrt{1+y^{2}}+3\sqrt{1+z^{2}}\geq 2\sqrt{10}$ https://booktoan.com/de-bai-cho-x2y3z2-chung-minh-rangsqrt1x22sqrt1y23sqrt1z2geq-2sqrt10.html https://booktoan.com/de-bai-cho-x2y3z2-chung-minh-rangsqrt1x22sqrt1y23sqrt1z2geq-2sqrt10.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-x2y3z2-chung-minh-rangsqrt1x22sqrt1y23sqrt1z2geq-2sqrt10.html https://booktoan.com/de-bai-cho-x2y3z2-chung-minh-rangsqrt1x22sqrt1y23sqrt1z2geq-2sqrt10.html/feed 0 Đề bài: Cho $n \in Z,n\geq 2;a_{1},a_{2},…,a_{n} \geq 0$.Chứng minh rằng:$\frac{a_{1}+a_{2}+…+a_{n} }{n}\geq \sqrt[n]{a_{1}a_{2}…a_{n} }$ https://booktoan.com/de-bai-cho-n-in-zngeq-2a_1a_2-a_n-geq-0-chung-minh-rangfraca_1a_2-a_n-ngeq-sqrtna_1a_2-a_n.html https://booktoan.com/de-bai-cho-n-in-zngeq-2a_1a_2-a_n-geq-0-chung-minh-rangfraca_1a_2-a_n-ngeq-sqrtna_1a_2-a_n.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-n-in-zngeq-2a_1a_2-a_n-geq-0-chung-minh-rangfraca_1a_2-a_n-ngeq-sqrtna_1a_2-a_n.html 0$Xét $f(x)=\ln x,x \in (0,+ \infty );$$f'(x)=\frac{1}{x};$$f”(x)=-\frac{1}{x^{2}}$\Rightarrow f$ là hàm số lồi […]]]> https://booktoan.com/de-bai-cho-n-in-zngeq-2a_1a_2-a_n-geq-0-chung-minh-rangfraca_1a_2-a_n-ngeq-sqrtna_1a_2-a_n.html/feed 0 Đề bài: Chứng minh rằng với $a, b, c, d, e$ là các số thực nằm trong khoảng $(0, 1)$ thì: $\left( {1 – a} \right)\left( {1 – b} \right)\left( {1 – c} \right)\left( {1 – d} \right)\left( {1 – e} \right) > 1 – a – b – c – d – e$ https://booktoan.com/de-bai-chung-minh-rang-voi-a-b-c-d-e-la-cac-so-thuc-nam-trong-khoang-0-1-thi-left-1-a-rightleft-1-b-rightleft-1-c-rightleft-1-d.html https://booktoan.com/de-bai-chung-minh-rang-voi-a-b-c-d-e-la-cac-so-thuc-nam-trong-khoang-0-1-thi-left-1-a-rightleft-1-b-rightleft-1-c-rightleft-1-d.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-voi-a-b-c-d-e-la-cac-so-thuc-nam-trong-khoang-0-1-thi-left-1-a-rightleft-1-b-rightleft-1-c-rightleft-1-d.html 1 – a – b – c – d – e\) Lời […]]]> https://booktoan.com/de-bai-chung-minh-rang-voi-a-b-c-d-e-la-cac-so-thuc-nam-trong-khoang-0-1-thi-left-1-a-rightleft-1-b-rightleft-1-c-rightleft-1-d.html/feed 0 Đề bài: Cho $k$ và $n$ là các số nguyên thỏa mãn $0 \le k \le n$. Chứng minh rằng: $C_{2n + k}^n.C_{2n – k}^n \le {\left( {C_{2n}^n} \right)^2}$ https://booktoan.com/de-bai-cho-k-va-n-la-cac-so-nguyen-thoa-man-0-le-k-le-n-chung-minh-rang-c_2n-kn-c_2n-kn-le-left-c_2nn-right2.html https://booktoan.com/de-bai-cho-k-va-n-la-cac-so-nguyen-thoa-man-0-le-k-le-n-chung-minh-rang-c_2n-kn-c_2n-kn-le-left-c_2nn-right2.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-k-va-n-la-cac-so-nguyen-thoa-man-0-le-k-le-n-chung-minh-rang-c_2n-kn-c_2n-kn-le-left-c_2nn-right2.html https://booktoan.com/de-bai-cho-k-va-n-la-cac-so-nguyen-thoa-man-0-le-k-le-n-chung-minh-rang-c_2n-kn-c_2n-kn-le-left-c_2nn-right2.html/feed 0 Đề bài: Cho $x,y,z$ là nghiệm của hệ $\begin{cases}x^2+y^2+z^2=8 (1) \\ xy+yz+zx=4 (2) \end{cases}$Chứng minh $-\frac{8}{3} \leq x;y;z \leq \frac{8}{3}$ https://booktoan.com/de-bai-cho-xyz-la-nghiem-cua-he-begincasesx2y2z28-1-xyyzzx4-2-endcaseschung-minh-frac8.html https://booktoan.com/de-bai-cho-xyz-la-nghiem-cua-he-begincasesx2y2z28-1-xyyzzx4-2-endcaseschung-minh-frac8.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-xyz-la-nghiem-cua-he-begincasesx2y2z28-1-xyyzzx4-2-endcaseschung-minh-frac8.html https://booktoan.com/de-bai-cho-xyz-la-nghiem-cua-he-begincasesx2y2z28-1-xyyzzx4-2-endcaseschung-minh-frac8.html/feed 0 Đề bài: Cho tứ diện $ABCD, P$ là một điểm tùy ý trong tứ diện. Gọi $A_1, B_1, C_1,D_1$ là hình chiếu của $P$ lên các mặt $BCD, ACD, ABD$ và $ABC$. Gọi $S$ và $r$ tương ứng là diện tích toàn phần và bán kính hình cầu nội tiếp tứ diện. Chứng minh: $\frac{S_{BCD}}{PA_1}+\frac{S_{CDA}}{PB_1}+\frac{S_{DAB}}{PC_1}+\frac{S_{ABC}}{PD_1} \geq \frac{S}{r}$ https://booktoan.com/de-bai-cho-tu-dien-abcd-p-la-mot-diem-tuy-y-trong-tu-dien-goi-a_1-b_1-c_1d_1-la-hinh-chieu-cua-p-len-cac-mat-bcd-acd-abd-va-abc-goi-s-va-r-tuong-ung-la-dien-tich-toan-phan-va-ba.html https://booktoan.com/de-bai-cho-tu-dien-abcd-p-la-mot-diem-tuy-y-trong-tu-dien-goi-a_1-b_1-c_1d_1-la-hinh-chieu-cua-p-len-cac-mat-bcd-acd-abd-va-abc-goi-s-va-r-tuong-ung-la-dien-tich-toan-phan-va-ba.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-tu-dien-abcd-p-la-mot-diem-tuy-y-trong-tu-dien-goi-a_1-b_1-c_1d_1-la-hinh-chieu-cua-p-len-cac-mat-bcd-acd-abd-va-abc-goi-s-va-r-tuong-ung-la-dien-tich-toan-phan-va-ba.html https://booktoan.com/de-bai-cho-tu-dien-abcd-p-la-mot-diem-tuy-y-trong-tu-dien-goi-a_1-b_1-c_1d_1-la-hinh-chieu-cua-p-len-cac-mat-bcd-acd-abd-va-abc-goi-s-va-r-tuong-ung-la-dien-tich-toan-phan-va-ba.html/feed 0