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a)3x-1=100+10 b)5^(2x-3)-50=75 c)(3x-16).7^5=2.7^6 d)(x-1)^5+3^2.5=72
3x=111 5^2x-3=75+50 3x-16=7^6:7^5.2 (x-1)^2=72-9.5
x=111:3 5^2x-3=125=5^3 3x-16=14 (x-1)^2=27
x=37 =>2x-3=3 3x=16+14 làm thành 2 trường hợp
2x=6 3x=30 .. .....
x=3 x=10
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\(1.\left(x-1\right)^2=4=\left(-2\right)^2=2^2\)
\(TH1:x-1=2\Rightarrow x=3\)
\(TH2:x-1=-2\Rightarrow x=-1\)
Vậy:...
\(2.\left(1+x\right)^2=9=\left(-3\right)^2=3^2\)
\(TH1:1+x=3\Rightarrow x=2\)
\(TH2:1+x=-3\Rightarrow x=-4\)
Vậy:....
\(3,\left(x+2019\right)^4=1\Rightarrow\left(x+2019\right)^4=1^4\)
\(\Rightarrow\orbr{\begin{cases}x+2019=1\\x+2019=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=-2018\\x=-2020\end{cases}}}\)
\(4,\left(x+10\right)^3=1\Rightarrow\left(x+10\right)^3=1^3\)
\(\Rightarrow x+10=1\)
\(\Rightarrow x=-9\)
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Bài làm
m) (x + 2).(3 - x) = 0;
=> x + 2 = 0 hoặc 3 - x = 0
=> x = -2 hoặc x = 3
Vậy x = -2 hoặc x = 3
d) 511.712 + 511.711
= 511 . ( 712 + 711 )
= 511 . [ 711 . ( 7 + 1 ) ]
= 511 . 711 . 8
= ( 5 . 7 )11 . 8
= 3511 . 8
512.712 + 9.511.711
= 511 ( 5 . 712 + 9 . 1 . 711 )
= 511 [ 711 ( 5 . 7 + 9 . 1 . 1 ) ]
= 511 ( 711 . 44 )
= 511 . 711 . 44
= 3511 . 44
m. \(\left(x+2\right)\left(3-x\right)=0\Leftrightarrow\orbr{\begin{cases}x+2=0\\3-x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)
d. \(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.\left(7^{12}+7^{11}\right)}{5^{11}.\left(5.7^{12}+9.7^{11}\right)}=\frac{7^{12}+7^{11}}{5.7^{12}+9.7^{11}}=\frac{1}{5.9}=\frac{1}{45}\)
q. \(\left(x-3\right)+\left(x-2\right)+\left(x-1\right)+...+10+11=11\)
\(\Rightarrow\left(x-3\right)+\left(x-2\right)+\left(x-1\right)+...+10=0\)
\(\Rightarrow\left[\left(x-3\right)+\left(x-2\right)+\left(x-1\right)\right]+(1+2+3+...+10)=0\)
\(\Rightarrow\left(x-3\right)+\left(x-2\right)+\left(x-1\right)+55=0\)
\(\Rightarrow x-3+x-2+x-1=-55\)
\(\Rightarrow3x-6=-55\)
\(\Rightarrow3x=-49\)
\(\Rightarrow x=-\frac{49}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,-2\left(x+7\right)+3\left(x-2\right)=-2\)
\(-2x-14+3x-6=-2\)
\(-2x+3x=-2+14+6\)
\(x=18\)
\(b,\left(x+3\right)^3:3-1=-10\)
\(\left(x+3\right)^3:3=-9\)
\(\left(x+3\right)^3=-27\)
\(\left(x+3\right)^3=\left(-9\right)^3\)
\(\Rightarrow x+3=9\)
\(\Rightarrow x=6\)
\(c,\left(x+1\right)^2\left(x^2+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+1=0\\x^2+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-1\\x^2=1\end{cases}\Rightarrow}\orbr{\begin{cases}x=-1\\x=1or-1\end{cases}}}\)
ko bt câu c này kl thế nào lun
`(x-10)^3 - (x-10)^4 = 0`
`=> (x-10)^3 . (1 - (x - 10)) = 0`
`=> (x-10)^3 . (1 - x +10) = 0`
`=> (x-10)^3 . (11-x) = 0`
`=> (x-10)^3 = 0` hoặc `11-x = 0`
`=> x - 10 = 0` hoặc `x = 11`
`=> x = 10` hoặc `x = 11`
Vậy `x` thuộc {`10;11`}
\(\left(x-10\right)^3-\left(x-10\right)^4=0\)
\(\left(x-10\right)^3\left(1-\left(x-10\right)\right)=0\)
\(\left(x-10\right)^3\left(1-x+10\right)=0\)
\(\left(x-10\right)^3\left(11-x\right)=0\)
\(x-10=0\) hoặc \(11-x=0\)
\(x=10\) hoặc \(x=11\)