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a) 127 - 2(-2x + 4)² = -1
2(-2x + 4)² = 127 + 1
2(-2x + 4)² = 128
(-2x + 4)² = 128 : 2
(-2x + 4)² = 64
-2x + 4 = 8 hoặc -2x + 4 = -8
*) -2x + 4 = 8
-2x = 8 - 4
-2x = 4
x = 4 : (-2)
x = -2
*) -2x + 4 = -8
-2x = -8 - 4
-2x = -12
x = -12 : (-2)
x = 6
b) -6² - 3.(-4 - x)³ = -39
3(-4 - x)³ = -6² + 39
3(-4 - x)³ = -36 + 39
3(-4 - x)³ = 3
(-4 - x)³ = 3 : 3
(-4 - x)³ = 1
(-4 - x)³ = 1³
-4 - x = 1
x = -4 - 1
x = -5
c) (-7x - 35).(2x² - 32) = 0
-7x - 35 = 0 hoặc 2x² - 32 = 0
*) -7x - 35 = 0
-7x = 0 + 35
-7x = 35
x = 35 : (-7)
x = -5
*) 2x² - 32 = 0
2x² = 0 + 32
2x² = 32
x² = 32 : 2
x² = 16
x = -4; x = 4
Vậy x = -5; x = -4; x = 4
d) (2018 + 2x)(4x² + 8) = 0
2018 + 2x = 0 (do 4x² + 8 > 0)
2x = 0 - 2018
2x = -2018
x = -2018 : 2
x = -1014
e) -145 - 4(3 - 2x)² = -245
4(3 - 2x) = -145 + 245
4(3 - 2x) = 100
3 - 2x = 100 : 4
3 - 2x = 25
2x = 3 - 25
2x = -22
x = -22 : 2
x = -11
g) 4(-x + 1)³ - (-5)² = -525
4(-x + 1)³ - 25 = -525
4(-x + 1)³ = -525 + 25
4(-x + 1)³ = -500
(-x + 1)³ = -500 : 4
(-x + 1)³ = -125
(-x + 1)³ = (-5)³
-x + 1 = -5
-x = -5 - 1
-x = -6
x = 6
7x x 49 = 750
7x x 72 = 750
7x = 750 : 72
7x = 750 - 2
7x = 748
⇒ x = 48
33.22 + 33.99 - 330
= 33.22 + 33.99 - 33.10
= 33. (22+99-10)
= 33.111
= 3663
33.22 + 33.99 - 330
= 33.22 + 33.99 - 33.10
=33( 22 + 99 - 10 )
= 33 . 111
= 3663
E = 1.2+2.3+3.4+......+99.100
Gấp E lên 3 lần ta có:
E . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
E . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
E . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 E . 3 = 99.100.101
E = 99.100.101 : 3
E = 33.100.101
E = 333 300
k mik nha
E = 1.2 + 2.3 + 3.4 + ... + 99.100
=> 3E = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
=> 3E = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 99.100.(101-98)
=> 3E = 1.2.3 - 0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
=> 3E = 99.100.101
=> E = 333300
Nếu \(p:3\left(dư1\right)\Rightarrow p+2⋮3\left(loại\right)\)
Nếu \(p:3\left(dư2\right)\Rightarrow p+4⋮3\left(loại\right)\)
Vậy p chia hết cho 3 mà p là số nguyên tố \(\Rightarrow p=3\)
\(\Rightarrow3^3+54=\left(2x-1\right)^2\)
\(\Leftrightarrow81=\left(2x-1\right)^2\)
\(\Leftrightarrow\left(2x-1\right)^2=9^2\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=9\\2x-1=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
Vậy \(x\in\left\{5;-4\right\}\).
a) \(\dfrac{2}{3}x-\dfrac{2}{3}=\dfrac{7}{12}-1\Leftrightarrow\dfrac{2}{3}x=\dfrac{7}{12}-1+\dfrac{2}{3}=\dfrac{1}{4}\Leftrightarrow x=\dfrac{3}{8}\)
b)\(\dfrac{1}{2}x+\dfrac{3}{5}\left(x-2\right)=3\Leftrightarrow\dfrac{1}{2}x+\dfrac{3}{5}x-\dfrac{6}{5}=3\Leftrightarrow\dfrac{11}{10}x=\dfrac{21}{5}\Leftrightarrow x=\dfrac{42}{11}\)
c)
\(\dfrac{3}{4}\left|x+5\right|+\dfrac{7}{8}=1\dfrac{1}{6}\Leftrightarrow\dfrac{3}{4}\left|x+5\right|=\dfrac{7}{6}-\dfrac{7}{8}=\dfrac{7}{24}\Leftrightarrow\left|x+5\right|=\dfrac{7}{18}\Leftrightarrow\left[{}\begin{matrix}x+5=\dfrac{7}{18}\\x+5=-\dfrac{7}{18}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{83}{18}\\x=-\dfrac{97}{18}\end{matrix}\right.\)
a) 23x−23=712−1⇔23x=712−1+23=14⇔x=3823x−23=712−1⇔23x=712−1+23=14⇔x=38
b)12x+35(x−2)=3⇔12x+35x−65=3⇔1110x=215⇔x=421112x+35(x−2)=3⇔12x+35x−65=3⇔1110x=215⇔x=4211
c)
34|x+5|+78=116⇔34|x+5|=76−78=724⇔|x+5|=718⇔⎡⎢ ⎢⎣x+5=718x+5=−718⇔⎡⎢ ⎢⎣x=−8318x=−9718