Tìm x:
a.(x-1)^x+2=(x-1)^x+4
b.1/4x2/6x3/8x4/10x5/12x...x30/62x31/42=2x
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12 tháng 10 2018
Bài 1:
a) \(\frac{8^2.4^5}{2^{20}}=\frac{\left(2^3\right)^2.\left(2^2\right)^5}{2^{20}}=\frac{2^{16}}{2^{20}}=\frac{1}{2^4}=\frac{1}{16}\)
...
đăng nhìu bài z con định giết ta đó ak :(
HT
12 tháng 10 2018
bài 1
b,81^1*3^17/27^10*9^15 c.(0,25)^3*8 d,cô giáo chữa rồi
=(3^4)^11*3^17/(3^3)^10*(3^2)15 =(0,25)^3*2^3
=3^44*3^17/3^30*3^30 =(0,25*2)^3
=3^61/3^60 =(1/2)^3
=3 =1/8
bài 2
a,(x-1)^3=27 b,x^2+x
(x-1)^3=3^3 x*(x+1)=0
x-1=3 x=0 hoặc x+1=0
x=4 vậy x=0 hoặc -1
c,(2x+1)^2=25
(2x+1)^2=(+-5)^2
TH1 2x+1=5 TH2: 2x+1=-5 d,e đến lp làm
2x=5-1 2x=-5-1
2x=4 2x=-6
x=4/2 x=-6/2
x=2 x=-3
AD
0
7 tháng 1 2023
Bài 2:
x^3+6x^2+12x+m chia hết cho x+2
=>x^3+2x^2+4x^2+8x+4x+8+m-8 chia hết cho x+2
=>m-8=0
=>m=8
3 tháng 10 2021
a: Ta có: \(\left(x-5\right)\left(x+3\right)=x\left(x-3\right)\)
\(\Leftrightarrow x^2-2x-15-x^2+3x=0\)
\(\Leftrightarrow x=15\)
b: Ta có: \(\left(x+2\right)^2=\left(x-1\right)\left(x+2\right)\)
\(\Leftrightarrow x+2=0\)
hay x=-2
c: Ta có: \(\left(x-6\right)\left(x+6\right)=x^2\)
\(\Leftrightarrow x^2-36=x^2\)(vô lý)
HP
3 tháng 10 2021
a. (x - 5)(x + 3) = x(x - 3)
<=> x2 + 3x - 5x - 15 = x2 - 3x
<=> x2 - x2 + 3x - 5x + 3x - 15 = 0
<=> x = 15
b. (x + 2)2 = (x - 1)(x + 2)
<=> x2 + 4x + 4 = x2 + 2x - x - 2
<=> x2 - x2 + 4x - 2x + x = -2 - 4
<=> 3x = -5
<=> \(x=\dfrac{-5}{3}\)
c. (x - 6)(x + 6) = x2
<=> x2 - 36 - x2 = 0
<=> x2 - x2 = 36
<=> 0 = 36 (vô lí)
Vậy nghiệm của PT là \(S=\varnothing\)
d. (2x - 3)2 = 4x2 - 8
<=> 4x2 - 12x + 9 - 4x2 + 8 = 0
<=> 4x2 - 4x2 - 12x = -8 - 9
<=> -12x = -17
<=> \(x=\dfrac{17}{12}\)
15 tháng 10 2021
c: \(x^4+x^3-4x^2+x+1\)
\(=x^4-x^3+2x^3-2x^2-2x^2+2x-x+1\)
\(=\left(x-1\right)\left(x^3+2x^2-2x-1\right)\)
\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+2x\left(x-1\right)\right]\)
\(=\left(x-1\right)^2\cdot\left(x^2+3x+1\right)\)
20 tháng 6 2021
`a)x^2>4`
`<=>sqrtx^2>sqrt4`
`<=>|x|>2`
`<=>` \(\left[ \begin{array}{l}x>2\\x<-2\end{array} \right.\)
`b)x^2<9`
`<=>\sqrtx^2<sqrt9`
`<=>|x|<3`
`<=>-3<x<3`
`c)(x-1)^2>=4`
`<=>\sqrt{(x-1)^2}>=sqrt4`
`<=>|x-1|>=2`
`<=>` \(\left[ \begin{array}{l}x-1 \ge 2\\x-1 \le -2\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x \ge 3\\x \le -1\end{array} \right.\)
`d)(1-2x)^2<=0,09`
`<=>\sqrt{(1-2x)^2}<=sqrt{0,09}`
`<=>|2x-1|<=0,3`
`<=>-0,3<=2x-1<=0,3`
`<=>0,7<=2x<=1,3`
`<=>0,35<=x<=0,65`
`e)x^2+6x-7>0`
`<=>x^2-x+7x-7>0`
`<=>x(x-1)+7(x-1)>0`
`<=>(x-1)(x+7)>0`
TH1:
\(\left[ \begin{array}{l}x-1>0\\x+7>0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x>1\\x>-7\end{array} \right.\)
`<=>x>1`
TH2"
\(\left[ \begin{array}{l}x-1<0\\x+7<0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x<1\\x<-7\end{array} \right.\)
`<=>x<-7`
`f)x^2-x<2`
`<=>x^2-x-2<0`
`<=>x^2-2x+x-2<0`
`<=>x(x-2)+x-2<0`
`<=>(x-2)(x+1)<0`
`<=>` \(\begin{cases}x-2<0\\x+1>0\\\end{cases}\)
`<=>` \(\begin{cases}x<2\\x>-1\\\end{cases}\)
`<=>-1<x<2`
20 tháng 6 2021
a) x2 > 4
<=> \(\left[{}\begin{matrix}x>2\\x< -2\end{matrix}\right.\)
b) \(x^2< 9\)
<=> \(-3< x< 3\)
c) \(\left(x-1\right)^2\ge4\)
<=> \(\left[{}\begin{matrix}x-1\ge2< =>x\ge3\\x-1\le-2< =>x\le-1\end{matrix}\right.\)
d) \(\left(1-2x\right)^2\le0,09\)
<=> \(-0,3\le1-2x\le0,3\)
<=> \(1,3\ge2x\ge0,7\)
<=> \(0,65\ge x\ge0,35\)
e) \(x^2+6x-7>0\)
<=> \(\left(x+7\right)\left(x-1\right)>0\)
<=> \(\left[{}\begin{matrix}x-1>0< =>x>1\\x+7< 0< =>x< -7\end{matrix}\right.\)
f) \(x^2-x< 2\)
<=> \(x^2-x-2< 0\)
<=> \(\left(x-2\right)\left(x+1\right)< 0\)
<=> \(\left\{{}\begin{matrix}x+1>0< =>x>-1\\x-2< 0< =>x< 2\end{matrix}\right.\)
<=> -1 < x < 2
g) \(4x^2-12x\le\dfrac{-135}{16}\)
<=> \(64x^2-192x+135\le0\)
<=> (8x - 15)(8x - 9) \(\le0\)
<=> \(\left\{{}\begin{matrix}8x-15\le0< =>x\le\dfrac{15}{8}\\8x-9\ge0< =>x\ge\dfrac{9}{8}\end{matrix}\right.\)
<=> \(\dfrac{9}{8}\le x\le\dfrac{15}{8}\)
C
3
31 tháng 7 2021
a) \(\text{5x(x-2)+(2-x)=0}\)
\(\Rightarrow5x\left(x-2\right)-\left(x-2\right)=0\\ \Rightarrow\left(x-2\right)\left(5x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\5x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{5}\end{matrix}\right.\)
b) \(\text{x(2x-5)-10x+25=0}\)
\(\Rightarrow x\left(2x-5\right)-5\left(2x-5\right)=0\\ \Rightarrow\left(x-5\right)\left(2x-5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\2x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=2,5\end{matrix}\right.\)
31 tháng 7 2021
c) \(\dfrac{25}{16}-4x^2+4x-1=0\)
\(\Rightarrow\dfrac{9}{16}-4x^2+4x=0\)
\(\Rightarrow-4x^2+4x+\dfrac{9}{16}=0\)
\(\Rightarrow-4x^2-\dfrac{1}{2}x+\dfrac{9}{2}x+\dfrac{9}{16}=0\)
\(\Rightarrow\left(-4x^2-\dfrac{1}{2}x\right)+\left(\dfrac{9}{2}x+\dfrac{9}{16}\right)=0\)
\(\Rightarrow-\dfrac{1}{2}x\left(8x+1\right)+\dfrac{9}{16}\left(8x+1\right)=0\)
\(\Rightarrow\left(-\dfrac{1}{2}x+\dfrac{9}{16}\right)\left(8x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}-\dfrac{1}{2}x+\dfrac{9}{16}=0\\8x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{9}{8}\\x=\dfrac{-1}{8}\end{matrix}\right.\)