HELP ME
4/5 - 2x = 2/5 + 3x
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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
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: \(x=-\frac{5}{12}\)
`(2(2-3x))/5<(4-2x)/3`
`<=>6(2-3x)<5(4-2x)`
`<=>3(2-3x)<5(2-x)`
`<=>6-9x<10-5x`
`<=>-4x<4`
`<=>x> -1`
a)\(2x^2\)+\(3\left(x^2-1\right)\)=\(5x\left(x+1\right)\)
\(2x^2\)+\(3x^2\)\(-3\)=\(5x^2+5x\)
\(5x^2-5x^2-5x=3\)
\(-5x=3\)
\(x=\frac{-3}{5}\)
tự ghi dấu suy ra ở đằng trước nhé
b) Vì \(2x\left(5-3x\right)=2x\left(3x-5\right)-3\left(x-7\right)=3\)
nên chỉ cần giải: \(6x^2-10x-3x+21=3\)
\(\Leftrightarrow6x^2-13x+21=3\)
\(\Leftrightarrow6x^2-13x+18=0\)
\(\Rightarrow\)pt vô nghiệm
\(\left(2x-\dfrac{3}{4}\right)^2=\left(3-x\right)^2\)
\(\Rightarrow2x-\dfrac{3}{4}=3-x\)
\(3x=3\dfrac{3}{4}\)
\(x=\dfrac{5}{4}\)
5(3x+5)-4(2x-3)=5x+3(2x+12)+1
15x+25-8x+12=5x+6x+36+1
7x+37=11x+37
7x+37-11x-37=0
-4x=0
x=0
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 \(x=\frac{3}{2}\)
\(\frac{4}{5}-2x=\frac{2}{5}+3x\)
\(\frac{4}{5}-\frac{2}{5}=2x+3x\)
\(\frac{2}{5}=5x\)
\(x=\frac{2}{25}\)
Ta có :\(\frac{4}{5}-2x=\frac{2}{5}+3x\)
\(\Leftrightarrow\) \(\frac{4}{5}-\frac{2}{5}=3.x+2.x\)
\(\Leftrightarrow\)\(\frac{2}{5}=5.x\)
\(\Leftrightarrow x=\frac{2}{5}:5\)
\(\Leftrightarrow x=\frac{2}{25}\)
~~~ AI NGANG QUA CHO CHÁU XIN 1 L~I~K~E~~~