Đặt \(x+1=t\Rightarrow x=t-1\)
\(P=\dfrac{3\left(t-1\right)^2-2\left(t-1\right)-1}{t^2}=\dfrac{3t^2-8t+4}{t^2}=\dfrac{4}{t^2}-\dfrac{8}{t}+3=4\left(\dfrac{1}{t}-1\right)^2-1\ge-1\)
\(P_{min}=-1\) khi \(t=1\Rightarrow x=0\)
Bài 1)tìm Min hay Max
a) G=\(\dfrac{2}{x^2+8}\)
b) H=\(\dfrac{-3}{x^2-5x+1}\)
Bài 2) Tìm Min hay Max
a)D=\(\dfrac{2x^2-16x+41}{x^2-8x+22}\)
b)E=\(\dfrac{4x^4-x^2-1}{\left(x^2+1\right)^2}\)
c)G=\(\dfrac{3x^2-12x+10}{x^2-4x+5}\)
Rút gọn các biểu thức sau :
A = \(2x^2\left(-3x^3+2x^2+x-1\right)+2x\left(x^2-3x+1\right)\)
B = \(2x:\dfrac{1}{2}x+x^2\)
C = \(\left[1:\left(1+x\right)+2x:\left(1-x^2\right)\right]:\left(\dfrac{1}{x}-1\right)\)
D = \(\dfrac{x^2-y^2}{x+y}.\dfrac{\left(x+y\right)^2}{x}+\dfrac{y^2}{x+y}.\dfrac{\left(x+y\right)^2}{x}\)
E = \(\dfrac{\left|x-3\right|}{x^2-9}.\left(x^2+6x+9\right)\)
F = \(\dfrac{\sqrt{x}}{\sqrt{x}-5}-\dfrac{10\sqrt{x}}{x-25}-\dfrac{5}{\sqrt{x}+5}\)
Giải các phương trình sau:
\(h.\dfrac{3\left(2x-1\right)}{4}-\dfrac{3x+1}{10}+1=\dfrac{2\left(3x+2\right)}{5}\)
\(i.\dfrac{\left(2x+1\right)^2}{5}-\dfrac{\left(x-1\right)^2}{3}=\dfrac{7x^2-14x-5}{15}\)
\(k.x+\dfrac{2x+\dfrac{x-1}{5}}{3}=1-\dfrac{3x-\dfrac{1-2x}{3}}{5}\)
a) Tìm min \(P=2x^2-8x+1\)
b) Tìm max \(Q=-5x^2-4x+1\)
c) Tìm min \(K=x\left(x-3\right)\left(x-4\right)\left(x-7\right)\)
d) Tìm min \(R=\frac{3x^2-8x+6}{x^2-2x+1}\)
Thực hiện phép tính:
a) \(3x.\left(2x^2-3x+4\right)\)
b) \(\left(x+3\right)^2+\left(3x-2\right)\left(x+4\right)\)
c) \(\dfrac{2x-4}{x-1}+\dfrac{2x+2}{x^2-1}\)
Cho biểu thức:
P = \(\left(\dfrac{x+1}{3x^2+3x}+\dfrac{1-2x}{6x^2-3x}-1\right)\): \(\dfrac{1-x}{2x}\)
a) Rút gọn P
b) Tìm x ∈ Z đề P có giá trị nguyên
c) Tìm x để P ≤ 1
a) \(x\left(x+4\right)-4x+1=0\)
b) \(2\left(x-3\right)+4=2x+2\)
c) \(\dfrac{x+3}{2}-\dfrac{2x+1}{4}=\dfrac{1}{4}\)
d) \(\dfrac{x^2+3x}{x+3}+3=0\)
e) \(x^2-3x\left(x-1\right)-3x-2=0\)
\(\dfrac{3}{x-5}-\dfrac{x+1}{x\left(x-5\right)}\)
\(\dfrac{8\left(y+2\right)}{3x^2}.\dfrac{15x^5}{4\left(y+2\right)^2}\)
\(\dfrac{8\left(y-1\right)}{3x^2-3}:\dfrac{4\left(y-1\right)^3}{x^2-2x+1}\)
Giải các phương trình sau:
1, \(\dfrac{x-1}{3}-x=\dfrac{2x-4}{4}\)
2, \(\left(x-2\right)\left(2x-1\right)=x^2-2x\)
3, \(3x^2-4x+1=0\)
4, \(\left|2x-4\right|=0\)
5, \(\left|3x+2\right|=4\)
6, \(\left|2x-5\right|=\left|-x+2\right|\)
*Giúp mình với mình đg cần gấp ạ T_T
