tìm x thuộc Z biết
a, (/x/ +3 ):5-3 =12
b, 86 : [2.(2x - 1 )2 - 7] +42 = 2.32
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12 tháng 7 2021
Bài 1:
a) Ta có: \(\dfrac{17}{6}-x\left(x-\dfrac{7}{6}\right)=\dfrac{7}{4}\)
\(\Leftrightarrow\dfrac{17}{6}-x^2+\dfrac{7}{6}x-\dfrac{7}{4}=0\)
\(\Leftrightarrow-x^2+\dfrac{7}{6}x+\dfrac{13}{12}=0\)
\(\Leftrightarrow-12x^2+14x+13=0\)
\(\Delta=14^2-4\cdot\left(-12\right)\cdot13=196+624=820\)
Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{14-2\sqrt{205}}{-24}=\dfrac{-7+\sqrt{205}}{12}\\x_2=\dfrac{14+2\sqrt{2015}}{-24}=\dfrac{-7-\sqrt{205}}{12}\end{matrix}\right.\)
b) Ta có: \(\dfrac{3}{35}-\left(\dfrac{3}{5}-x\right)=\dfrac{2}{7}\)
\(\Leftrightarrow\dfrac{3}{5}-x=\dfrac{3}{35}-\dfrac{10}{35}=\dfrac{-7}{35}=\dfrac{-1}{5}\)
hay \(x=\dfrac{3}{5}-\dfrac{-1}{5}=\dfrac{3}{5}+\dfrac{1}{5}=\dfrac{4}{5}\)
10 tháng 12 2021
\(a,\) Vì \(x,y\in Z\) nên \(\left(3x+2\right):3R2;R1\)
Mà \(\left(3x+2\right)\left(y-8\right)=12\) nên \(3x+2\inƯ\left(12\right)=\left\{-12;-6;-4;-3;-2;-1;1;2;3;4;6;12\right\}\)
Do đó \(3x+2\in\left\{-4;-1;2\right\}\)
\(\Rightarrow x\in\left\{-2;-1;0\right\}\)
Với \(x=-2\Rightarrow\left(-4\right)\left(y-8\right)=12\Rightarrow y-8=-3\Rightarrow y=5\)
Với \(x=-1\Rightarrow\left(-3\right)\left(y-8\right)=12\Rightarrow y-8=-4\Rightarrow y=4\)
Với \(x=0\Rightarrow2\left(y-8\right)=12\Rightarrow y-8=6\Rightarrow y=14\)
Vậy PT có nghiệm \(\left(x;y\right)\) là \(\left(-2;5\right);\left(-1;4\right);\left(0;14\right)\)
10 tháng 12 2021
\(b,\) Vì \(x,y\in Z\) nên \(\left(5x-4\right):5R1;R4\)
Mà \(\left(5x-4\right)\left(y+3\right)=-18\)
\(\Rightarrow5x-4\inƯ\left(-18\right)=\left\{-18;-9;-6;-3;-2;-1;1;2;3;6;9;18\right\}\\ \Rightarrow5x-4\in\left\{-9;1;6\right\}\\ \Rightarrow x\in\left\{-1;1;2\right\}\)
Với \(x=-1\Rightarrow-9\left(y+3\right)=-18\Rightarrow y+3=2\Rightarrow y=-1\)
Với \(x=1\Rightarrow y+3=18\Rightarrow y=15\)
Với \(x=2\Rightarrow6\left(y+3\right)=18\Rightarrow y+3=3\Rightarrow y=0\)
Vậy PT có nghiệm \(\left(x;y\right)\) là \(\left(-1;-1\right);\left(1;15\right);\left(2;0\right)\)
TV
1
AH
Akai Haruma
Giáo viên
30 tháng 10 2021
Lời giải:
a. Đề có cả x,y. Bạn xem lại
b.
PT $\Leftrightarrow 5x(x-3)-2(x-3)=0$
$\Leftrightarrow (x-3)(5x-2)=0$
$\Leftrightarrow x-3=0$ hoặc $5x-2=0$
$\Leftrightarrow x=3$ hoặc $x=\frac{2}{5}$
c.
PT $\Leftrightarrow (7x-2)(x-4)=0$
$\Leftrightarrow 7x-2=0$ hoặc $x-4=0$
$\Leftrightarrow x=\frac{2}{7}$ hoặc $x=4$
d. Đề thiếu.
QT
1
AH
Akai Haruma
Giáo viên
29 tháng 12 2023
Lời giải:
$86:(2.5x-1-7)+42=2.32=64$
$86:(10x-8)+42=64$
$86:(10x-8)=64-42=22$
$10x-8=86:22=\frac{43}{11}$
$10x=\frac{43}{11}+8=\frac{131}{11}$
$x=\frac{131}{11}:10=\frac{131}{110}$
HB
1
21 tháng 12 2016
\(86:\left[2.\left(2x-1\right)^2-7\right]+4^2=2.3^2\)
\(86:\left[2.\left(2x-1\right)^2-7\right]+16=2.9\)
\(86:\left[2.\left(2x-1\right)^2-7\right]=2\)
\(2.\left(2x-1\right)^2-7=43\)
\(2.\left(2x-1\right)^2=50\)
\(\left(2x+1\right)^2=25=5^2=\left(-5\right)^2\)
\(\Rightarrow\orbr{\begin{cases}2x+1=5\\2x+1=-5\end{cases}\Rightarrow\orbr{\begin{cases}2x=4\\2x=-6\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\\x=-3\end{cases}}}\)
DN
2
T
14 tháng 9 2023
\(a,\dfrac{3}{7}-x=\dfrac{1}{2}x-3\)
\(\Rightarrow-x-\dfrac{1}{2}x=-3-\dfrac{3}{7}\)
\(\Rightarrow-\dfrac{3}{2}x=-\dfrac{24}{7}\)
\(\Rightarrow x=-\dfrac{24}{7}:\left(-\dfrac{3}{2}\right)\)
\(\Rightarrow x=\dfrac{16}{7}\)
\(b,5x-\dfrac{2}{3}=\dfrac{5}{3}-2x\)
\(\Rightarrow5x+2x=\dfrac{5}{3}+\dfrac{2}{3}\)
\(\Rightarrow7x=\dfrac{7}{3}\)
\(\Rightarrow x=\dfrac{7}{3}:7\)
\(\Rightarrow x=\dfrac{1}{3}\)
#Toru
14 tháng 9 2023
a: 3/7-x=1/2x-3
=>-3/2x=-3+3/7
=>-1/2x=-1+1/7=-6/7
=>1/2x=6/7
=>x=6/7*2=12/7
b: =>5x+2x=5/3+2/3
=>7x=7/3
=>x=1/3
24 tháng 12 2023
`#3107.101107`
`1.`
`a,`
`(2x - 3)^2 = |3 - 2x|`
`=> (2x - 3)^2 = |2x - 3|`
`=>`\(\left[{}\begin{matrix}2x-3=\left(2x-3\right)^2\\2x-3=-\left(2x-3\right)^2\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}2x-3-\left(2x-3\right)^2=0\\2x-3+\left(2x-3\right)^2=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}\left(2x-3\right)\left(1-2x+3\right)=0\\\left(2x-3\right)\left(1+2x-3\right)=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}2x-3=0\\4-2x=0\\2x-2=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=2\\x=1\end{matrix}\right.\)
Vậy, `x \in {3/2; 2; 1}`
`b,`
`(x - 1)^2 + (2x - 1)^2 = 0`
`=>`\(\left[{}\begin{matrix}\left(x-1\right)^2=0\\\left(2x-1\right)^2=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x-1=0\\2x-1=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=1\\x=\dfrac{1}{2}\end{matrix}\right.\)
Vậy, `x \in {1; 1/2}`
`c,`
`5 - x^2 = 1`
`=> x^2 = 4`
`=> x^2 = (+-2)^2`
`=> x = +-2`
Vậy, `x \in {-2; 2}`
`d,`
`x - 2\sqrt{x} = 0`
`=> x^2 - (2\sqrt{x})^2 = 0`
`=> x^2 - 4x = 0`
`=> x(x - 4) = 0`
`=>`\(\left[{}\begin{matrix}x=0\\x-4=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
Vậy, `x \in {0; 4}`
`g,`
`(x - 1) + 1/7 = 0`
`=> x - 1 + 1/7 = 0`
`=> x - 6/7 = 0`
`=> x = 6/7`
Vậy, `x = 6/7.`
PN
4
21 tháng 1 2022
a: =>2x-x=-5/2-1/3
=>x=-17/6
b: =>4(x-2)2=36
=>(x-2)2=9
=>x-2=3 hoặc x-2=-3
hay x=5 hoặc x=-1
c: =>2x+1/2=5/6
=>2x=1/3
hay x=1/6
a) \(\left(\left|x\right|+3\right):5-3=12\Leftrightarrow\left|x\right|+3=45\Leftrightarrow\orbr{\begin{cases}x=42\\x=-42\end{cases}}\)
b) \(86:\left[2\left(2x-1\right)^2-7\right]+4^2=2\cdot3^2\Leftrightarrow2\left(2x-1\right)^2-7=43\Leftrightarrow\left(2x-1\right)^2=25\Leftrightarrow\orbr{\begin{cases}2x-1=-5\\2x-1=5\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)
a) \(\left(\left|x\right|+3\right)\div5-3=12\)
\(\left(\left|x\right|+3\right)\div5=12+3\)
\(\left(\left|x\right|+3\right)\div5=15\)
\(\left|x\right|+3=15.5\)
\(\left|x\right|+3=75\)
\(\left|x\right|=75-3\)
\(\left|x\right|=72\)
\(\Rightarrow\orbr{\begin{cases}x=72\\x=-72\end{cases}}\)
Vậy \(x\in\left\{72;-72\right\}\)
b) \(86\div\left[2,\left(2x-1\right)^2-7\right]+4^2=2.3^2\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]+16=18\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]=18-16\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]=2\)
\(2.\left(2x-1\right)^2-7=86\div2\)
\(2.\left(2x-1\right)^2-7=43\)
\(2.\left(2x-1\right)^2=43+7\)
\(2.\left(2x-1\right)^2=50\)
\(\left(2x-1\right)^2=50\div2\)
\(\left(2x-1\right)^2=25\)
\(\left(2x-1\right)^2=5^2\)
\(\Rightarrow2x-1=5\)
\(2x=5+1\)
\(2x=6\)
\(x=6\div2\)
\(x=3\)