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25 tháng 6 2018
Nhiều câu quá >.<
a/ \(2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20.\)
\(2x^2+10x=x^2+6x+9+x^2-2x+1+20.\)
\(10x=4x+30\)
\(6x=30\Rightarrow x=5\)
các câu còn lại tương tự
25 tháng 6 2018
\(a,2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20\)
\(\Leftrightarrow2x^2+10x=x^2+6x+9+x^2-2x+1+20\)
\(\Leftrightarrow2x^2+10x=2x^2+4x+30\)
\(\Leftrightarrow2x^2+10x-2x^2-4x=30\)
\(\Leftrightarrow6x=30\)
\(\Leftrightarrow x=5\)
Vậy ...........
\(b,\left(2x-2\right)^2=\left(x+1\right)^2+3\left(x-2\right)\left(x+5\right)\)
\(\Leftrightarrow4x^2-8x+4=x^2+2x+1+3x^2+15x-6x-30\)
\(\Leftrightarrow4x^2-8x+4=4x^2+11x-29\)
\(\Leftrightarrow4x^2-8x-4x^2-11x=-29-4\)
\(\Leftrightarrow-19x=-33\)
\(\Leftrightarrow x=\frac{33}{19}\)
Vậy...........
\(c,\left(x-1\right)^2+\left(x+3\right)^2=2\left(x-2\right)\left(x+1\right)+38\)
\(\Leftrightarrow x^2-2x+1+x^2+6x+9=2x^2+2x-4x-4+38\)
\(\Leftrightarrow2x^2+4x+10=2x^2-2x+34\)
\(\Leftrightarrow2x^2+4x-2x^2+2x=34-10\)
\(\Leftrightarrow6x=24\)
\(\Leftrightarrow x=4\)
Vậy.............
\(d,\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-1\right)-18\)
\(\Leftrightarrow x^3+6x+12x+8-\left(x^3-6x+12x-8\right)=12x^2-12x-8\)
\(\Leftrightarrow x^3+6x+12x+8-x^3+6x-12x+8=12x^2-12x-8\)
\(\Leftrightarrow12x=-24\)
\(\Leftrightarrow x=-2\)
Vậy............
16 tháng 12 2016
a)Đặt \(A=3-3^2+3^3-3^4+...+3^{95}-3^{96}\)
\(3A=3^2-3^3+3^4-3^5+...+3^{96}-3^{97}\)
\(3A+A=\left(3^2-3^3+3^4-3^5+...+3^{96}-3^{97}\right)+\left(3-3^2+3^3-3^4+...+3^{95}-3^{96}\right)\)
\(4A=-3^{97}+3\)
\(A=\frac{-3^{97}+3}{4}\)
b)tương tự như câu a
c)\(\left(100-1^2\right)\left(100-2^2\right)\left(100-3^2\right).....\left(100-99^2\right)\)
\(=\left(10^2-1^2\right)\left(10^2-2^2\right)\left(10^2-3^2\right)....\left(10^2-10^2\right)...\left(10^2-99^2\right)\)
\(=\left(10^2-1^2\right)\left(10^2-2^2\right)\left(10^2-3^2\right)...0...\left(10^2-99^2\right)\)
=0
2 tháng 10 2016
b) \(3.2^{x+1}=12\)
\(2^{x+1}=12:3\)
\(2^{x+1}=4\)
\(2^{x+1}=2^2\)
\(x+1=2\)
\(x=2-1\)
\(x=1\)
Vậy \(x=1\)
c) \(2^{x-1}=2^3+2^4-2^3\)
\(2^{x-1}=8+16-8\)
\(2^{x-1}=16\)
\(2^{x-1}=2^4\)
\(x-1=4\)
\(x=5\)
Vậy \(x=5\)
d) \(x^{50}=x\)
\(x^{50}-x=0\)
\(\Rightarrow x\in\left\{0;1\right\}\)
Vậy \(x\in\left\{0;1\right\}\)
HC
2 tháng 10 2016
\(b.3.2^{x+1}=12\\ \Rightarrow2^{x+1}=4\\ \Rightarrow2^{x+1}=2^2\\ \Rightarrow x=1\\ \)
c) \(2^{x-1}=2^3-2^3+2^4\\ \Rightarrow2^{x-1}=0+16\\ \Rightarrow2^{x-1}=16\\ \Rightarrow2^{x-1}=2^4\\ \Rightarrow x-1=4\\ \Rightarrow x=5\)
d) \(x^{50}=x\\ \Rightarrow x=0;1\)
e) \(2\left(2x-1\right)^4=32\\ \Rightarrow\left(2x-1\right)^4=16\\ \Rightarrow\left(2x-1\right)^4=2^4\\ \Rightarrow2x-1=2\\ \Rightarrow2x=3\\ \Rightarrow x=\frac{3}{2}\)
g) Bí
NQ
2
23 tháng 7 2015
a) \(2^{x-1}+2^{x+1}+2^{x+2}=104\)
=> \(2^{x-1}+2^x\cdot2+2^x\cdot2^2=104\)
=> \(2^x:2+2^x\cdot\left(2+2^2\right)=104\)
=> \(2^x\cdot\frac{1}{2}+2^x\cdot6=104\)
=> \(2^x\cdot\left(\frac{1}{2}+6\right)=104\Rightarrow2^x=104:\left(\frac{1}{2}+6\right)=104:\frac{13}{2}=16\)
=> \(x=4\)
MV
5 tháng 5 2017
2.
\(\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot5\cdot3\cdot37\right)\\=\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-\left(13\cdot5\right)\cdot\left(3\cdot37\right)\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-65\cdot111\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot0\\ =0\)
HQ
14 tháng 11 2020
a) 3x.3x+2 =81
3x.3x.32 =81
3x.3x.9 =81
3x.3x =81/9
3x.3x =9
31.31 =9
x =1
b)2(x+15)+3(x+25)=2050
2(x+15)+3(x+15+10)=2050
2(x+15)+3(x+15)+3.10=2050
(x+15)(2+5)+30=2050
(x+15)5=2050-30
(x+15)5=2020
x+15=2020/5
x+15=404
x =404-15
x =389
c)2x+2x+1+2x+2+2x+3=960
2x+2x.2+2x.22+2x.23=960
2x(1+2+22+23)=960
2x(1+2+4+8)=960
2x.15=960
2x =960/15
2x =64
26 =64
x =6
bài d làm tương tự c,e làm tương tự a
f)3x.32x+3=729
33x.33=729
33x.27 =729
33x =729/27
33x =27
33.1 =27
x =1
12 tháng 8 2022
1: =>-2x+6x2-4x+8=3/2+18x2
=>\(18x^2+\dfrac{3}{2}=6x^2-6x+8\)
\(\Leftrightarrow12x^2+6x-\dfrac{13}{2}=0\)
hay \(x\in\left\{\dfrac{-3+\sqrt{87}}{12};\dfrac{-3-\sqrt{87}}{12}\right\}\)
2: Đề thiếu vế phải rồi bạn
3: \(\Leftrightarrow x^2\cdot\dfrac{2}{3}-2x-\dfrac{4}{3}x+4=\dfrac{2}{3}x^2-\dfrac{2}{3}x\)
=>-10/3x+2/3x=-4
=>-8/3x=-4
=>x=4:8/3=4x3/8=12/8=3/2
\(3+2\left|x-2\right|=2^3-\left(-1\right)\)
\(\Rightarrow3+2\left|x-2\right|=8+1\)
\(\Rightarrow2\left|x-2\right|=9-3\)
\(\Rightarrow2\left|x-2\right|=6\)
\(\Rightarrow\left|x-2\right|=6\div2\)
\(\Rightarrow\left|x-2\right|=3\)
\(\Rightarrow\orbr{\begin{cases}x-2=-3\\x-2=3\end{cases}}\)
\(\text{Trường hợp : }x-2=-3\)
\(\Rightarrow x=-3+2\)
\(\Rightarrow x=-1\)
\(\text{Trường hợp : }x-2=3\)
\(\Rightarrow x=3+2\)
\(\Rightarrow x=5\)
\(\text{Vậy }x\in\left\{-1;5\right\}\)
\(3+2.\left|x-2\right|=2^3-\left(-1\right)\)
\(\Leftrightarrow3+2.\left|x-2\right|=2^3+1\)
\(\Leftrightarrow3+2.\left|x-2\right|=8+1\)
\(\Leftrightarrow3+2.\left|x-2\right|=9\)
\(\Leftrightarrow2.\left|x-2\right|=9-3\)
\(\Leftrightarrow2.\left|x-2\right|=6\)
\(\Leftrightarrow\left|x-2\right|=6:2\)
\(\Leftrightarrow\left|x-2\right|=3\)
Xét 2 TH:
TH1:
x - 2 = -3
x = -3 + 2
x = -1
TH2:
x - 2 = 3
x = 3 + 2
x = 5
\(\Rightarrow\orbr{\begin{cases}x=-1\\x=5\end{cases}}\)