|3x + 2| + |1 - 2x| = 5 - |x|
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\(\left(2x-\dfrac{3}{4}\right)^2=\left(3-x\right)^2\)
\(\Rightarrow2x-\dfrac{3}{4}=3-x\)
\(3x=3\dfrac{3}{4}\)
\(x=\dfrac{5}{4}\)
a. \(3-4x\left(25-2x\right)-8x^2+x-300=0\)
\(\Leftrightarrow3-100x+8x^2-8x^2+x-300=0\)
\(\Leftrightarrow-297-99x=0\)
\(\Leftrightarrow x=3\)
Vậy \(n_0\) của PT là: x=3
b. \(\Leftrightarrow\frac{\left(2-6x\right)}{5}-2+\frac{3x}{10}=7-\frac{3x+3}{4}\)
\(\Leftrightarrow\frac{\left(4-12x\right)}{5}-\frac{20}{10}+\frac{3x}{10}=\frac{\left(28-3x-3\right)}{4}\)
\(\Leftrightarrow\frac{\left(-16-9x\right)}{10}=\frac{\left(25-3x\right)}{4}\)
\(\Leftrightarrow-64-36x=250-30x\)
\(\Leftrightarrow-6x=314\)
\(\Leftrightarrow x=-\frac{157}{3}\)
Vậy -\(n_0\) của PT là: \(x=\frac{-157}{3}\)
c. \(5x+\frac{2}{6}-8x-\frac{1}{3}=4x+\frac{2}{5}-5\)
\(\Leftrightarrow-3x=4x-\frac{23}{5}\)
\(\Leftrightarrow7x=\frac{23}{5}\)
\(\Leftrightarrow x=\frac{23}{35}\)
Vậy \(n_0\) của PT là: \(x=\frac{23}{35}\)
d. \(3x+\frac{2}{3}-3x+\frac{1}{6}=2x+\frac{5}{3}\)
\(\Leftrightarrow\frac{5}{6}=2x+\frac{5}{3}\)
\(\Leftrightarrow x=-\frac{5}{12}\)
Vậy \(n_0\) của Pt là: \(x=-\frac{5}{12}\)
*Gọi a=x-1, b=2x-3, c=3x-5.
-Phương trình trở thành:
a3+b3+c3-3abc=0 ⇔(a+b)3+c3-3ab(a+b)-3abc=0
⇔(a+b+c)[(a+b)2-c(a+b)+c2]-3ab(a+b+c)=0
⇔(a+b+c)(a2+2ab+b2-ac-bc+c2-3ab)=0
⇔(a+b+c)(a2+b2+c2-ab-ac-bc)=0
⇔a+b+c=0 hay a2+b2+c2-ab-ac-bc=0
*a+b+c=0 ⇔x-1+2x-3+3x-5=0 ⇔6x-9=0 ⇔x=\(\dfrac{3}{2}\)
*a2+b2+c2-ab-ac-bc=0
Vì a2+b2+c2-ab-ac-bc≥0 và dấu bằng xảy ra khi và chỉ khi a=b=c nên
=>x-1=2x-3 ⇔x=2
=>x-1=3x-5 ⇔x=2
=>2x-3=3x-5⇔ x=2
Tìm x:
1. 3x (2x + 3) - (2x + 5).(3x - 2) = 8
\(\Leftrightarrow6x^2+9x-6x^2+4x-15x+10=0 \)
\(\Leftrightarrow-2x+10=0\Leftrightarrow x=5\)
Vậy x = 5
2. 4x (x -1) - 3(x2 - 5) -x2 = (x - 3) - (x + 4)
\(\Leftrightarrow4x^2-4x-3x^2+15-x^2=x-3-x-4\)
\(\Leftrightarrow-4x+15=-7\)
\(\Leftrightarrow-4x=-22\Leftrightarrow x=\frac{11}{2}\)
Vậy x = \(\frac{11}{2}\)
3. 2 (3x -1) (2x +5) - 6 (2x - 1) (x + 2) = -6
\(\Leftrightarrow2\left(6x^2+15x-2x-5\right)-6\left(2x^2+4x-x-2\right)=-6\)
\(\Leftrightarrow12x^2+30x-4x-10-12x^2-24x+6x+12=-6\)
\(\Leftrightarrow8x=-8\Leftrightarrow x=-1\)
Vậy x = -1
4. 3 ( 2x - 1) (3x - 1) - (2x - 3) (9x - 1) - 3 = -3
\(\Leftrightarrow3\left(6x^2-2x-3x+1\right)-18x^2+2x+27x-3-3=-3\)
\(\Leftrightarrow18x^2-6x-9x+3-18x^2+2x+27x-6=-3\)
\(\Leftrightarrow14x=0\Leftrightarrow x=0\)
Vậy x = 0
5. (3x - 1) (2x + 7) - ( x + 1) (6x - 5) = (x + 2) - (x - 5)
\(\Leftrightarrow6x^2+21x-2x-7-6x^2+5x-6x+5=7\)
\(\Leftrightarrow18x=9\Leftrightarrow x=\frac{1}{2}\)
Vậy x = \(\frac{1}{2}\)
6. 3xy (x + y) - (x + y) (x2 + y2 + 2xy) + y3 = 27
\(\Leftrightarrow3x^2y+3xy^2-\left(x+y\right)^3+y^3=27\)
\(\Leftrightarrow3x^2y+3xy^2-x^3-y^3-3x^2y-3xy^2+y^3=27\)
\(\Leftrightarrow-x^3=27\)
\(\Leftrightarrow x=-3\)
Vậy x = -3
7. 3x (8x - 4) - 6x (4x - 3) = 30
\(\Leftrightarrow24x^2-12x-24x^2+12x=30\)
\(\Leftrightarrow0=30\) ( vô lý)
Vậy pt vô nghiệm
8. 3x (5 - 2x) + 2x (3x - 5) = 20
\(\Leftrightarrow15x-6x^2+6x^2-10x=20\)
\(\Leftrightarrow5x=20\Leftrightarrow x=4\)
Vậy x = 4
Câu 1:
\(M=x^2-3x+5\)
\(M=x^2-2.\frac{3}{2}x+\frac{9}{4}+\frac{11}{4}\)
\(M=\left(x-\frac{3}{2}\right)^2+\frac{11}{4}\ge\frac{11}{4}\)
Dấu = xảy ra khi \(x-\frac{3}{2}=0\Rightarrow x=\frac{3}{2}\)
Vậy Min M = 11/4 khi x=3/2
b)\(N=2x^2+3x\)
\(N=2\left(x^2+\frac{3}{2}x\right)\)
\(N=2\left(x^2+2.\frac{3}{4}x+\frac{9}{16}\right)-\frac{9}{8}\)
\(N=2\left(x+\frac{3}{4}\right)^2-\frac{9}{8}\ge-\frac{9}{8}\)
Dấu = xảy ra khi \(x+\frac{3}{4}=0\Rightarrow x=-\frac{3}{4}\)
Vậy MIn N = -9/8 khi x=-3/4
c)Tự làm nha
Ta có : x2 - 3x + 5
= x2 - 2.x.\(\frac{3}{2}\) + \(\frac{3}{2}^2\) + \(\frac{11}{4}\)
= \(\left(x-\frac{3}{2}\right)^2+\frac{11}{4}\)
Vì \(\left(x-\frac{3}{2}\right)^2\ge0\forall x\in R\)
Nên : \(\left(x-\frac{3}{2}\right)^2+\frac{11}{4}\) \(\ge\frac{11}{4}\forall x\in R\)
Vậy GTNN của biểu thức là : \(\frac{11}{4}\) khi \(x=\frac{3}{2}\)
a) Ta có : |2x - 5| = x + 1
\(\Leftrightarrow\orbr{\begin{cases}2x-5=-x-1\\2x-5=x+1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x+x=-1+5\\2x-x=1+5\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3x=4\\x=6\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=6\end{cases}}\)
Thôi giúp luôn =.=
\(\left(x+3\right)^2+\left(2x+1\right)\left(3x-5\right)-2x\left(3-x\right)+4x+25\)
\(=x^2+6x+9+6x^2-10x+3x-5-6x+2x^2+4x+25\)
\(=9x^2-3x+29\)
Ai chẳng biết chuyển vế đổi dấu :v
a) \(x-7=4x+10\)
\(x-4x=10+7\)
\(-3x=17\)
\(x=\dfrac{17}{-3}\)
Vậy \(x=\dfrac{17}{-3}\)
b) \(2x+5=-3x+7\)
\(2x+3x=7-5\)
\(5x=2\)
\(x=\dfrac{2}{5}\)
Vậy \(x=\dfrac{2}{5}\)
c) \(x-\left(3x+7\right)=6x-1\)
\(x-3x-7=6x-1\)
\(-2x-7=6x+1\)
\(-7-1=6x+2x\)
\(-8=8x\)
\(x=\dfrac{-8}{8}=-1\)
Vậy \(x=-1\)
d) \(x+\left(5x-1\right)=15\)
\(x+5x-1=15\)
\(6x=15+1\)
\(6x=16\)
\(x=\dfrac{16}{6}=\dfrac{8}{3}\)
Vậy \(x=\dfrac{8}{3}\)
1 , x - 7 = 4x + 10
x - 4x = 10 + 7
- 3x = 17
x = 17 : ( - 3 )
x = \(\dfrac{-17}{3}\)
2 , 2x + 5 = -3x + 7
2x + 3x = 7 -5
5x = 2
x = 2 : 5
x =\(\dfrac{2}{5}\)
3 , x - ( 3x + 7 ) = 6x - 1
x - 3x - 7 = 6x - 1
x - 3x -6x = -1 +7
-8x = 6
x = 6 : ( -8 )
x = \(\dfrac{-3}{4}\)
4 , x + ( 5x -1 ) = 15
x + 5x - 1 = 15
x + 5x = 15 + 1
6x = 16
x = 16 : 6
x = \(\dfrac{8}{3}\)
5 , / x + 1 / = / 2x - 5 /
TH 1 : x + 1 = 2x - 5
x - 2x = -5 -1
- x = -4
= > x = 4
TH 2 : -x -1 = -2x + 5
-x + 2x = 5 + 1
x = 6
6 , / 3x + 8 / - / x -10 / = 0
3x + 8 - x + 10 = 0
3x - x = 0 - 10 - 8
2 x = -18
x = -18 : 2
x = - 9
a)2x-1=3x+5
⇔ 2x -3x = 5 +1
⇔ -x = 6
⇔ x = -6
Vậy x= -6
b)2(x-3)+1=3(1-x)+2
⇔ 2x -6 +1 = 3 -3x +2
⇔ 2x - 5 = 5 -3x
⇔ 2x +3x = 5 +5
⇔ 5x = 10
⇔ x = 2
Vậy x= 2