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a) (x - 2)^2 = 16
(x - 2)^2 = 4^2 = (-4)^2
=> x - 2 = 4 hoặc x - 2 = -4
- Nếu x - 2 = 4
=> x = 4 + 2 = 6
- Nếu x - 2 = -4
=> x = (-4) + 2 = -2
Vậy x = 6 hoặc x = -2
b) (2x - 1)^3 = 8
(2x - 1)^3 = 2^3
=>2x - 1 = 2
2x = 2 + 1 = 3
\(x=\frac{3}{2}\)
c) (2x - 1)^4 = 81
(2x - 1)^4 = 3^4=(-3)^4
=> 2x - 1 = 3 hoặc 2x - 1 = -3
- Nếu 2x - 1 = 3
=>2x = 3 + 1 = 4
=>x = 4 : 2 = 2
- Nếu 2x - 1 = -3
2x = (-3) + 1 = -2
x = -1
Vậy x = 2 hoặc x = -1
1a) x - 7 = -18
=> x = -18 + 7
=> x = -11
b) -2x + 8 = -24
=> -2x = -24 - 8
=> -2x = -32
=> x = -32 : (-2)
=> x = 16
c) 4 - 2x = 59
=> 2x = 4 - 59
=> 2x = -55
=> x = -55 : 2
=> x = -27,5
d) -36 - x = 59
=> x = -36 - 59
=> x = -95
k) -81 : x = (-3)
=> x = -81 : (-3)
=> x = 27
g) -16 : x = 2
=> x = -16 : 2
=> x = -8
m) (6 - 27) - (3 - x) = (-7) . (-8)
=> -21 - (3 - x) = 56
=> 3 - x = -21 - 56
=> 3 - x = -77
=> x = 3 + 77
=> x = 80
a)
200 - ( 2 . x + 6 ) = 8 . 2
200 - ( 2 . x + 6 ) = 16
2 . x + 6 = 200 - 16
2 . x + 6 = 184
x + 6 = 184 : 2
x + 6 = 92
x = 92 - 6
x = 86
b)
2 . x : 4 = 16
x : 4 = 16 : 2
x : 4 = 8
x = 8 . 4
x = 32
c)
2008 . x : 2008 . 5 = 2008 . 3
2008. ( x : 5 ) = 6024
x : 5 = 6024 : 2008
x : 5 = 3
x = 3 . 5
x = 15
a) \(\dfrac{2x+5}{2x+1}=\dfrac{2x+1+4}{2x+1}=\dfrac{2x+1}{2x+1}+\dfrac{4}{2x+1}=1+\dfrac{4}{2x+1}\)
Để \(\dfrac{2x+5}{2x+1}\in Z\) thì \(\dfrac{4}{2x+1}\in Z\)
\(\Rightarrow4\) ⋮ \(2x+1\)
\(\Rightarrow2x+1\inƯ\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)
\(\Rightarrow2x\in\left\{0;-2;1;-3;3;-5\right\}\)
\(\Rightarrow x\in\left\{0;-1;\dfrac{1}{2};-\dfrac{3}{2};\dfrac{3}{2};-\dfrac{5}{2}\right\}\)
Mà x nguyên \(\Rightarrow\text{x}\in\left\{0;-1\right\}\)
b) \(\dfrac{3x+5}{x+1}=\dfrac{3x+3+2}{x+1}=\dfrac{3\left(x+1\right)+2}{x+1}=\dfrac{3\left(x+1\right)}{x+1}+\dfrac{2}{x+1}=3+\dfrac{2}{x+1}\)
Để \(\dfrac{3x+5}{x+1}\in Z\) thì \(\dfrac{2}{x+1}\in Z\)
\(\Rightarrow2\) ⋮ \(x+1\)
\(\Rightarrow x+1\inƯ\left(2\right)=\left\{1;-1;2;-2\right\}\)
\(\Rightarrow x\in\left\{0;-2;1;-3\right\}\)
c) \(\dfrac{3x+8}{x-1}=\dfrac{3x-3+11}{x-1}=\dfrac{3\left(x-1\right)+11}{x-1}=\dfrac{3\left(x-1\right)}{x-1}+\dfrac{11}{x-1}=3+\dfrac{11}{x-1}\)
Để: \(\dfrac{3x+8}{x-1}\in Z\) thì \(\dfrac{11}{x-1}\in Z\)
\(\Rightarrow11\) ⋮ \(x-1\)
\(\Rightarrow x-1\inƯ\left(11\right)=\left\{1;-1;11;-11\right\}\)
\(\Rightarrow x\in\left\{2;0;12;-10\right\}\)
d) \(\dfrac{5x+12}{x-2}=\dfrac{5x-10+22}{x-2}=\dfrac{5\left(x-2\right)+22}{x-2}=\dfrac{5\left(x-2\right)}{x-2}+\dfrac{22}{x-2}=5+\dfrac{22}{x-2}\)
Để: \(\dfrac{5x+12}{x-2}\in Z\) thì \(\dfrac{22}{x-2}\in Z\)
\(\Rightarrow22\) ⋮ \(x-2\)
\(\Rightarrow x-2\inƯ\left(22\right)=\left\{1;-1;2;-2;11;-11;22;-22\right\}\)
\(\Rightarrow x\in\left\{3;1;4;0;13;-9;24;-20\right\}\)
e) \(\dfrac{7x-12}{x+16}=\dfrac{7x+112-124}{x+16}=\dfrac{7\left(x+16\right)-124}{x+16}=\dfrac{7\left(x+16\right)}{x+16}-\dfrac{124}{x+16}=7-\dfrac{124}{x+16}\)
Để \(\dfrac{7x-12}{x+16}\in Z\) thì \(\dfrac{124}{x+16}\in Z\)
\(\Rightarrow124\) ⋮ \(x+16\)
\(\Rightarrow x+16\inƯ\left(124\right)=\left\{1;-1;2;-2;4;-4;31;-31;62;-62;124;-124\right\}\)
\(\Rightarrow x\in\left\{-15;-17;-14;-18;-12;-20;15;-47;46;-78;108;-140\right\}\)
\(a)\frac{5}{8}-x=2\frac{1}{6}\)
\(\Rightarrow\frac{5}{8}-x=\frac{13}{6}\)
\(\Rightarrow x=\frac{5}{8}-\frac{13}{6}\)
\(\Rightarrow x=\frac{15}{24}-\frac{52}{24}\)
\(\Rightarrow x=-\frac{37}{24}\)
\(b)\) \(\frac{4}{9}:x=-\frac{1}{3}+1\frac{1}{6}\)
\(\Rightarrow\frac{4}{9}:x=-\frac{1}{3}+\frac{7}{6}\)
\(\Rightarrow\frac{4}{9}:x=-\frac{2}{6}+\frac{7}{6}\)
\(\Rightarrow\frac{4}{9}:x=\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{9}:\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{9}.\frac{6}{5}\)
\(\Rightarrow x=\frac{8}{15}\)
\(c)\left(3x-2\right)^3=-\frac{1}{27}\)
\(\Rightarrow3x-2=-\frac{1}{3}\)
\(\Rightarrow3x=-\frac{1}{3}+2\)
\(\Rightarrow3x=-\frac{1}{3}+\frac{6}{3}\)
\(\Rightarrow3x=\frac{5}{3}\)
\(\Rightarrow x=\frac{5}{3}:3\)
\(\Rightarrow x=\frac{5}{9}\)
d ) và e ) tự làm
Chúc bạn học tốt !!!
\(-8.\left(2x-1\right)+4.x=16\)
\(-16x+8+4x=16\)
\(-12x=16-8\)
\(-12x=8\)
\(x=\frac{-2}{3}\)
vậy \(x=\frac{-2}{3}\)
học vui Cô Nàng Kim Ngưu
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