√21-x^2-4x=x+3
Giải các bất phương trình, hệ phương trình
a) \(\dfrac{x^2-4x+3}{2x-3}\ge x-1\)
b) \(3x^2-\left|4x^2+x-5\right|>3\)
c)\(4x-\left|2x^2-8x-15\right|\le-1\)
d)\(x+3-\sqrt{21-4x-x^2}\ge0\)
e)\(\left\{{}\begin{matrix}x\left(x+5\right)< 4x+2\\\left(2x-1\right)\left(x+3\right)\ge4x\end{matrix}\right.\)
f)\(\dfrac{1}{x^2-5x+4}\le\dfrac{1}{x^2-7x+10}\)
giải bpt : \(\sqrt{-x^2-4x+21}< x+3\)
ĐK: \(-7\le x\le3\)
\(\sqrt{-x^2-4x+21}< x+3\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+3>0\\-x^2-4x+21< x^2+6x+9\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>-3\\2x^2+10x-12>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>-3\\\left(x+6\right)\left(x-1\right)>0\end{matrix}\right.\)
\(\Leftrightarrow x>1\)
\(\Rightarrow x\in(1;3]\)
2 TÌM X
X- 9 = 21:5
X = ............................
X = ............................
X : 3 = 1,248 : 4
X = ..........................
X = ............................
X- 9 = 21:5
X- 9 = 4,2
x = 4,2 + 9
x = 13,2
X : 3 = 1,248 : 4
X : 3 = 0,312
x = 0,312 x 3
x = 0,936
x - 9 = 4,2
x = 4,2 + 9 =13,2
x : 3 = 0,312
x = 0,312 x 3 = 0,936
1.Giải toán bằng dạng phương trình chứa dấu giá trị tuyệt đối a.|3-7x|=2 b.|4x-3|=2x c.|2x-3|=-4x d.|3x-2|=-x+21 e.|4x-1|=x-2 f.|x+16|=3x-2
tìm GTNN
A=(x^2 -3x+1) . (x^2-3x-2) +2018
B=(x-1)(x+5)(x^2+4x+5)=2018
C=15-4x^2+4x
D=(x-1)(x-3)=21
giải pt :a,\(\left(2x+6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
Tìm x, biết :
a, ( x +2 ) ( x^2 - 2x + 4 ) - x( x + 3 ) ( x - 3) = 26
b, ( x - 3 ) ( x^2 + 3x + 9 ) - x( x - 4 ) ( x + 4 ) = 21
c, ( 2x -1 ) ( 4x^2 + 2x + 1 ) - 4x(2x^2 - 3 ) = 23
a/\(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x+3\right)\left(x-3\right)=26\)
↔ \(x^3+2^3\)\(-x\left(x^2-3^2\right)\)= 26
↔\(x^3+8-x^3+9x=26\)
↔\(9x=18\leftrightarrow x=2\)
Vậy x=2
b/\(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-4\right)\left(x+4\right)=21\)
\(\Leftrightarrow x^3-3^3-x\left(x^2-4^2\right)=21\)
\(\Leftrightarrow x^3-9-x^3+16x=21\)
\(\Leftrightarrow16x=30\)
\(\Leftrightarrow x=\frac{15}{8}\)
Vậy \(x=\frac{15}{8}\)
c/\(\left(2x-1\right)\left(4x^2+2x+1\right)-4x\left(2x^2-3\right)=23\)
↔\(\left(2x\right)^3-1^3-4x\left(2x^2-3\right)=23\)
↔\(8x^3-1-8x^3+12x=23\)
↔\(12x=24\leftrightarrow x=2\)
Vậy x=2
a, (x + 2)(x2 - 2x + 4 ) - x(x + 3)(x - 3) = 26
<=> x3 + 8 - x(x2 - 9) = 26
<=> x3 + 8 - x3 + 9x = 26
<=> 9x - 18 = 0
<=> 9x = 18
<=> x = 2
b, (x - 3)(x2 + 3x + 9) - x(x - 4)(x + 4) = 21
<=> x3 - 27 - x(x2 - 16) = 21
<=> x3 - 27 - x3 + 16x = 21
<=> 16x - 48 = 0
<=> 16x = 48
<=> x = 3
c, (2x - 1)(4x2 + 2x + 1) - 4x(2x2 - 3) = 23
<=> 8x3 - 1 - 8x3 + 12x = 23
<=> 12x - 24 = 0
<=> 12x = 24
<=> x = 2
\(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x+3\right)\left(x-3\right)=26\)
\(< =>x^3-2x^2+4x+2x^2-4x+8-x\left(x^2-9\right)-26=0\)
\(< =>x^3+8-x^3+9x-26=0\)
\(< =>9x-18=0< =>x=2\)
=>36(2x+3)=x^4+16x^2+441-8x^3+42x^2-168x
=>x^4-8x^3+58x^2-240x+333=0
=>(x-3)^2*(x^2-2x+37)=0
=>x-3=0
=>x=3
tìm GTNN
A=(x^2 -3x+1) . (x^2-3x-2) +2018
B=(x-1)(x+5)(x^2+4x+5)=2018
C=15-4x^2+4x
D=(x-1)(x-3)=21
\(C=-\left(4x^2-4x-15\right)\)
\(=-\left(4x^2-4x+1-16\right)\)
\(=-\left(2x-1\right)^2+16< =16\)
Dấu = xảy ra khi x=1/2
\(D=x^2-4x+3+21\)
\(=x^2-4x+4+20=\left(x-2\right)^2+20>=20\)
Dấu '=' xảy ra khi x=2