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a: \(\Leftrightarrow\left[{}\begin{matrix}x>3\\x< -4\end{matrix}\right.\)
b: -2<x<5
a) \(\left(x+2\right)^3-x^2\left(x+6\right)=0\)
\(\Leftrightarrow x^3+6x^2+12x+8-x^3-6x^2=0\)
\(\Leftrightarrow12x+8=0\)
\(\Leftrightarrow12x=-8\)
\(\Leftrightarrow x=-\dfrac{8}{12}\)
\(\Leftrightarrow x=-\dfrac{2}{3}\)
b) \(\left(2x+3\right)^3-8x\left(x+1\right)\left(x-1\right)=9x\left(4x-3\right)\)
\(\Leftrightarrow8x^3+36x^2+54x+27-8x\left(x^2-1\right)=36x^2-27x\)
\(\Leftrightarrow8x^3+36x^2+54x+27-8x^3+8x=36x^2-27x\)
\(\Leftrightarrow8x^3-8x^3+36x^2-36x^2+54x+27x+8x+27=0\)
\(\Leftrightarrow89x+27=0\)
\(\Leftrightarrow x=-\dfrac{27}{89}\)
c) \(\left(2-x\right)^3+\left(2+x\right)^3-12x\left(x+1\right)=0\)
\(\Leftrightarrow8-12x+6x^2-x^3+8+12x+6x^2+x^3-12x^2-12x=0\)
\(\Leftrightarrow\left(x^3-x^3\right)+\left(6x^2+6x^2-12x^2\right)-\left(12x-12x\right)+12x+\left(8+8\right)=0\)
\(\Leftrightarrow12x+16=0\)
\(\Leftrightarrow x=-\dfrac{16}{12}\)
\(\Leftrightarrow x=-\dfrac{4}{3}\)
`#040911`
`a)`
`(x + 2)^3 - x^2(x + 6) = 0`
`<=> x^3 + 6x^2 + 12x + 8 - x^3 - 6x^2 = 0`
`<=> (x^3 - x^3) + (6x^2 - 6x^2) + 12x = 0`
`<=> 12x = 0`
`<=> x = 0`
Vậy, `x = 0.`
`b)`
`(2x + 3)^3 - 8x(x - 1)(x + 1) = 9x(4x - 3)`
`<=> 8x^3 + 36x^2 + 54x + 27 - 8x(x^2 - 1) = 36x^2 - 27x`
`<=> 8x^3 + 36x^2 + 54x + 27 - 8x^3 + 8x - 36x^2 + 27x = 0`
`<=> (8x^3 - 8x^3) + (36x^2 - 36x^2) + (54x + 8x + 27x) + 27 = 0`
`<=> 89x + 27 = 0`
`<=> 89x = -27`
`<=> x = -27/89`
Vậy, `x = -27/89`
`c)`
`(2 - x)^3 + (2 + x)^3 - 12x(x + 1) = 0`
`<=> 8 - 12x + 6x^2 - x^3 + 8 + 12x + 6x^2 + x^3 - 12x^2 - 12x = 0`
`<=> (-x^3 + x^3) + (12x - 12x - 12x) + (6x^2 + 6x^2 - 12x^2) + (8 + 8)=0`
`<=> -12x + 16 = 0`
`<=> -12x = -16`
`<=> 12x = 16`
`<=> x=4/3`
Vậy, `x = 4/3.`
c: \(\Leftrightarrow\left(x-5\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)
Bài 1:
a: \(=6x^3-10x^2+6x\)
b: \(=-2x^3-10x^2-6x\)
Bài 4:
a: =>3x+10-2x=0
=>x=-10
c: =>3x2-3x2+6x=36
=>6x=36
hay x=6
Bài 1:
\(a,=6x^3-10x^2+6x\\ b,=-2x^3-10x^2-6x\)
Bài 4:
\(a,\Leftrightarrow3x+10-2x=0\Leftrightarrow x=-10\\ b,\Leftrightarrow x\left(2x^2+9x-5\right)-\left(2x^3+9x^2+x+4,5\right)=3,5\\ \Leftrightarrow2x^3+9x^2-5x-2x^3-9x^2-x-4,5=3,5\\ \Leftrightarrow-6x=8\Leftrightarrow x=-\dfrac{4}{3}\\ c,\Leftrightarrow3x^2-3x^2+6x=36\Leftrightarrow x=6\)
Bài 1:
\(a,=7xy\left(2x-3y+4xy\right)\\ b,=x\left(x+y\right)-5\left(x+y\right)=\left(x-5\right)\left(x+y\right)\\ c,=\left(x-y\right)\left(10x+8\right)=2\left(5x+4\right)\left(x-y\right)\\ d,=\left(3x+1-x-1\right)\left(3x+1+x+1\right)\\ =2x\left(4x+2\right)=4x\left(2x+1\right)\\ e,=5\left[\left(x-y\right)^2-4z^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\\ f,=x^2+8x-x-8=\left(x+8\right)\left(x-1\right)\\ g,\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\\ =\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\\ h,=x^2+3x+x+3=\left(x+3\right)\left(x+1\right)\)
a)\(\left(\frac{3}{5}\right)^5\times x=\left(\frac{3}{7}\right)^7\)
\(\Leftrightarrow\frac{3^5}{5^5}\times x=\frac{3^7}{7^7}\)
\(\Leftrightarrow x=\frac{3^7}{7^7}:\frac{3^5}{5^5}\)
\(\Leftrightarrow x=\frac{3^7\times5^5}{7^7\times3^5}\)
\(\Leftrightarrow x=\frac{3^2\times5^5}{7^7}\)
b)\(\left(\frac{-1}{3}\right)^3\times x=\frac{1}{81}\)
\(\Leftrightarrow\frac{\left(-1\right)^3}{3^3}\times x=\frac{1}{3^4}\)
\(\Leftrightarrow x=\frac{1}{3^4}:\frac{-1}{3^3}\)
\(\Leftrightarrow x=\frac{1\times3^3}{3^4\times\left(-1\right)}\)
\(\Leftrightarrow x=\frac{1}{-3}\)
c)\(\Leftrightarrow\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)
\(\Leftrightarrow x-\frac{1}{2}=\frac{1}{3}\)
\(\Leftrightarrow x=\frac{1}{3}+\frac{1}{2}\)
\(\Leftrightarrow x=\frac{5}{6}\)
d)\(\Leftrightarrow\left(x+\frac{1}{2}\right)^4=\left(\frac{2}{3}\right)^4\)
\(\Leftrightarrow x+\frac{1}{2}=\frac{2}{3}\)
\(\Leftrightarrow x=\frac{2}{3}-\frac{1}{2}\)
\(\Leftrightarrow x=\frac{1}{6}\)
a) \(3^x\cdot3=243\)
\(\Rightarrow3^{x+1}=243\)
\(\Rightarrow3^{x+1}=3^5\)
\(\Rightarrow x+1=5\)
\(\Rightarrow x=4\)
b) \(2^x\cdot162=1024\)
Xem lại đề
c) \(64\cdot4^x=168\)
Xem lại đề
d) \(2^x=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
a: =>3^x=81
=>x=4
b: =>2^x=1024/16^2=4
=>x=2
c: =>4^x=16^8/64=4^16/4^3=4^13
=>x=13
a, 3 x + 1 : 3 4 = 81
3 x - 3 = 3 4
x – 3 = 4
x = 7
Vậy x = 7
b, 3 x + 3 . 3 x + 1 = 729
3 2 x + 4 = 3 6
2x + 4 = 6
x = 1
Vậy x = 1
c, 2 x + 3 . 2 x = 128
2 2 x + 3 = 2 7
2x + 3 = 7
x = 2
Vậy x = 2
d, 23 + 3 x = 5 6 : 5 3
23 + 3 x = 5 3
23 + 3x = 125
3x = 102
x = 34
Vậy x = 34
e, 2 x + 2 x + 4 = 272
2 x + 2 x . 2 4 = 272
2 x ( 1 + 2 4 ) = 272
2 x . 17 = 272
2 x = 16
2 x = 2 4
x = 4
Vậy x = 4