Cho x,y,z là ba số không âm thỏa mãn: x + y + z = 1. Chứng minh rằng:

\(\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}\le\frac{9}{10}\)

giải bất phương trình sau:

\(\left|\frac{5}{x+2}\right|< \left|\frac{10}{x-1}\right|\)

(nói rõ cách giải giúp mình, vì có nhiều chỗ mình chưa hiểu)

Giải các Phtr sau ☘Tiểu Tuyết☘

a) 26x3 - 12x2 + 13x = 6

b) (x + 1)3 - ( x - 1)3 = 6 ( x2 + x + 1)

c) \(\frac{3x-1}{x-1}-\frac{2x+5}{x+3}-\frac{8}{x^2+2x-3}=1\)

Tính nhanh

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tim so co ba chu so, biet rang khi viet them chu so 1 vao ben trai so do thi duoc so co bon chu so gap 9lan so phai tim.

bai giai

\(\sqrt{2x-1}\) = \(x\) + 1

Chứng minh bất đẳng thức:
\(a^{^{ }2}+b^2+c^2+\dfrac{3}{4}\ge a+b+c\)

Đề kiểm tra - Đề 2 - Câu 2 (SBT trang 200)

Cho điểm \(M\left(1;-2\right)\) và đường thẳng \(\Delta\) có phương trình :

\(3x-4y-1=0\)

a) Tìm tọa độ điểm M' đối xứng với M qua đường thẳng \(\Delta\)

b) Viết phương trình đường thẳng \(\Delta'\) đối xứng với \(\Delta\) qua điểm M

c) Viết phương trình đường tròn tâm M và tiếp xúc với đường thẳng \(\Delta\)

Bài 10 (SBT trang 189)

Biết \(\sin\alpha=\dfrac{3}{4}\) và \(\dfrac{\pi}{2}< \alpha< \pi\). Tính :

a) \(A=\dfrac{2\tan\alpha-3\cot\alpha}{\cos\alpha+\tan\alpha}\)

b) \(B=\dfrac{\cos^2\alpha+\cot^2\alpha}{\tan\alpha-\cot\alpha}\)

Bài 9 (SBT trang 189)

Tính các giá trị lượng giác của góc \(\alpha\), nếu :

a) \(\cos\alpha=-\dfrac{1}{4},\pi< \alpha< \dfrac{3\pi}{2}\)

b) \(\sin\alpha=\dfrac{2}{3},\dfrac{\pi}{2}< \alpha< \pi\)

c) \(\tan\alpha=\dfrac{7}{3},0< \alpha< \dfrac{\pi}{2}\)

d) \(\cot\alpha=-\dfrac{14}{9},\dfrac{3\pi}{2}< \alpha< 2\pi\)