Tìm x, biết:
a) x − 1 5 2 + 17 25 = 26 25
b) 1 5 27 + 3 x − 7 9 3 = 24 27
Bài 4. Tìm số nguyên x , biết:
a) |x - 2|= 0 b) |x + 3|= 1 c) -3 |4 - x|= -9 d) |2x + 1|= -2
Bài 5. Tìm số nguyên x, biết:
a) (x + 3)mũ 2 = 36 b) (x + 5)mũ 2 =100 c) (2x - 4)mũ 2 = 0 d) (x - 1)mũ 3 = 27
tìm x, biết:
a) (x-2)^x-3(x+1)(x-1)+6x^2=5
a) (x-2)^x-3(x+1)(x-1)+6x^2=5
<=> \(x^2-4x+4-3(x^2-1)+6x^2-5=0\)
<=>\(x^2-4x+4-3x^2+3+6x^2-5=0\)
<=>\(4x^2-4x+2=0\)
<=> \(4x^2-4x+1+1=0\)
<=>\((2x-1)^2+1=0\)
\(ta\) có \((2x-1)^2 > hoặc = 0\)
1>0
=> \((2x-1)^2+1=0 (vô lí)\)
=> phuơng trình vô nghiêm S={ rỗng }
Bài 10: Tìm các số nguyên \(x\) biết:
a) \(2x-3\) là bội của \(x+1\)
b) \(x-2\) là ước của \(3x-2\)
Bài 14: Tìm số tự nhiên \(n\) sao cho:
a) \(4n-5\) ⋮ \(2n-1\)
b) \(n^2+3n+1\) ⋮ \(n+1\)
Bài 16: Tìm cặp số tự nhiên \(x\),\(y\) biết:
a) \(\left(x+5\right)\left(y-3\right)=15\)
b) \(\left(2x-1\right)\left(y+2\right)=24\)
c) \(xy+2x+3y=0\)
d) \(xy+x+y=30\)
Bài 10:
a: 2x-3 là bội của x+1
=>\(2x-3⋮x+1\)
=>\(2x+2-5⋮x+1\)
=>\(-5⋮x+1\)
=>\(x+1\in\left\{1;-1;5;-5\right\}\)
=>\(x\in\left\{0;-2;4;-6\right\}\)
b: x-2 là ước của 3x-2
=>\(3x-2⋮x-2\)
=>\(3x-6+4⋮x-2\)
=>\(4⋮x-2\)
=>\(x-2\inƯ\left(4\right)\)
=>\(x-2\in\left\{1;-1;2;-2;4;-4\right\}\)
=>\(x\in\left\{3;1;4;0;6;-2\right\}\)
Bài 14:
a: \(4n-5⋮2n-1\)
=>\(4n-2-3⋮2n-1\)
=>\(-3⋮2n-1\)
=>\(2n-1\inƯ\left(-3\right)\)
=>\(2n-1\in\left\{1;-1;3;-3\right\}\)
=>\(2n\in\left\{2;0;4;-2\right\}\)
=>\(n\in\left\{1;0;2;-1\right\}\)
mà n>=0
nên \(n\in\left\{1;0;2\right\}\)
b: \(n^2+3n+1⋮n+1\)
=>\(n^2+n+2n+2-1⋮n+1\)
=>\(n\left(n+1\right)+2\left(n+1\right)-1⋮n+1\)
=>\(-1⋮n+1\)
=>\(n+1\in\left\{1;-1\right\}\)
=>\(n\in\left\{0;-2\right\}\)
mà n là số tự nhiên
nên n=0
Bài 16:
a: \(\left(x+5\right)\left(y-3\right)=15\)
=>\(\left(x+5\right)\left(y-3\right)=1\cdot15=15\cdot1=\left(-1\right)\cdot\left(-15\right)=\left(-15\right)\cdot\left(-1\right)=3\cdot5=5\cdot3=\left(-3\right)\cdot\left(-5\right)=\left(-5\right)\cdot\left(-3\right)\)
=>\(\left(x+5;y-3\right)\in\left\{\left(1;15\right);\left(15;1\right);\left(-1;-15\right);\left(-15;-1\right);\left(3;5\right);\left(5;3\right);\left(-3;-5\right);\left(-5;-3\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(-4;18\right);\left(10;4\right);\left(-6;-12\right);\left(-20;2\right);\left(-2;8\right);\left(0;6\right);\left(-8;-2\right);\left(-10;0\right)\right\}\)
mà (x,y) là cặp số tự nhiên
nên \(\left(x,y\right)\in\left\{\left(10;4\right);\left(0;6\right)\right\}\)
b: x là số tự nhiên
=>2x-1 lẻ và 2x-1>=-1
\(\left(2x-1\right)\left(y+2\right)=24\)
mà 2x-1>=-1 và 2x-1 lẻ
nên \(\left(2x-1\right)\cdot\left(y+2\right)=\left(-1\right)\cdot\left(-24\right)=1\cdot24=3\cdot8\)
=>\(\left(2x-1;y+2\right)\in\left\{\left(-1;-24\right);\left(1;24\right);\left(3;8\right)\right\}\)
=>\(\left(2x;y\right)\in\left\{\left(0;-26\right);\left(2;22\right);\left(4;6\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(0;-26\right);\left(1;11\right);\left(2;6\right)\right\}\)
mà (x,y) là cặp số tự nhiên
nên \(\left(x,y\right)\in\left\{\left(1;11\right);\left(2;6\right)\right\}\)
c:
x,y là các số tự nhiên
=>x+3>=3 và y+2>=2
xy+2x+3y=0
=>\(xy+2x+3y+6=6\)
=>\(x\left(y+2\right)+3\left(y+2\right)=6\)
=>\(\left(x+3\right)\left(y+2\right)=6\)
mà x+3>=3 và y+2>=2
nên \(\left(x+3\right)\cdot\left(y+2\right)=3\cdot2\)
=>x=0 và y=0
d: xy+x+y=30
=>\(xy+x+y+1=31\)
=>\(x\left(y+1\right)+\left(y+1\right)=31\)
=>\(\left(x+1\right)\left(y+1\right)=31\)
\(\Leftrightarrow\left(x+1\right)\cdot\left(y+1\right)=1\cdot31=31\cdot1=\left(-1\right)\cdot\left(-31\right)=\left(-31\right)\cdot\left(-1\right)\)
=>\(\left(x+1;y+1\right)\in\left\{\left(1;31\right);\left(31;1\right);\left(-1;-31\right);\left(-31;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(0;30\right);\left(30;0\right);\left(-2;-32\right);\left(-32;-2\right)\right\}\)
mà (x,y) là cặp số tự nhiên
nên \(\left(x,y\right)\in\left\{\left(0;30\right);\left(30;0\right)\right\}\)
Tìm X, biết:
A) X x 2/5 + 1/2 x X = 9
B) 1/9 : X + 3/9 : X =5/7
a: \(x\cdot\dfrac{2}{5}+\dfrac{1}{2}\cdot x=9\)
=>\(x\left(\dfrac{2}{5}+\dfrac{1}{2}\right)=9\)
=>\(x\cdot\dfrac{9}{10}=9\)
=>\(x=9:\dfrac{9}{10}=10\)
b: \(\dfrac{1}{9}:x+\dfrac{3}{9}:x=\dfrac{5}{7}\)
=>\(\left(\dfrac{1}{9}+\dfrac{3}{9}\right):x=\dfrac{5}{7}\)
=>\(\dfrac{4}{9}:x=\dfrac{5}{7}\)
=>\(x=\dfrac{4}{9}:\dfrac{5}{7}=\dfrac{4}{9}\cdot\dfrac{7}{5}=\dfrac{28}{45}\)
Bài 4: Tìm số nguyên , biết:
a) x/2 = 2/4
b) -1/5 = 2/x
c) x/5 = 5/x
Bài 4:
a) \(\dfrac{x}{2}=\dfrac{2}{4}\)
\(\Rightarrow\dfrac{x}{2}=\dfrac{1}{2}\)
\(\Rightarrow x=2\)
Vậy: \(x=2\)
b) \(-\dfrac{1}{5}=\dfrac{2}{x}\)
\(\Rightarrow x=\dfrac{-5.2}{1}=-10\)
Vậy: \(x=-10\)
c) \(\dfrac{x}{5}=\dfrac{5}{x}\)
\(\Rightarrow x^2=25\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
Vậy: \(x\in\left\{5;-5\right\}\)
\(\dfrac{x}{2}=\dfrac{2}{4}\\ =>x=\dfrac{2.2}{4}=1\)
\(\dfrac{-1}{5}=\dfrac{2}{x}\\ =>x=\dfrac{2.5}{-1}=-10\)
\(\dfrac{x}{5}=\dfrac{5}{x}\\ =>x^2=25\\ x=5;x=-5\)
Bài 3: Tìm x, biết:
a)(3x-5)(5-3x)+9(x+1)2=30
b)(x+4)2-(x+1)(x-1)=16
b. (x + 4)2 - (x + 1)(x - 1) = 16
<=> x2 + 4x + 16 - (x2 - 1) = 16
<=> x2 + 4x + 16 - x2 + 1 - 16 = 0
<=> x2 - x2 + 4x = 16 - 16 - 1
<=> 4x = -1
<=> x = \(\dfrac{-1}{4}\)
\(a,\Leftrightarrow-9x^2+30x-25+9x^2+18x+9=30\\ \Leftrightarrow48x=46\\ \Leftrightarrow x=\dfrac{23}{24}\\ b,\Leftrightarrow x^2+8x+16-x^2+1=16\\ \Leftrightarrow8x=-1\Leftrightarrow x=-\dfrac{1}{8}\)
bài 2:tìm x, biết:
a. x + 1^3 = 2^5 - ( -1^3 )
b. 3^7 - x = 1^4 - ( -3^5 )
a) \(x+1^3=2^5-\left(-1^3\right)\)
\(\Rightarrow x+1=33\)
=> x = 32
b) \(3^7-x=1^4-\left(-3^5\right)\)
\(\Rightarrow2187-x=1+243=244\)
=> x = 1943
a) \(\Leftrightarrow x+1=32+1\)
\(\Leftrightarrow x=32\)
Vậy x = 32
b) \(\Leftrightarrow2187-x=1+243\)
\(\Leftrightarrow2187-x=244\)
\(\Leftrightarrow x=1943\)
Vậy x = 1943
a) \(x+1^3=2^5-\left(-1^3\right)\)
\(x+1=32-\left(-1\right)\)
\(x+1=33\)
\(x=33-1\)
\(x=32\)
b) \(3^7-x=1^4-\left(-3^5\right)\)
\(2187-x=1-\left(-243\right)\)
\(2187-x=244\)
\(x=2187-244\)
\(x=1943\)
Tìm x,biết:
a)5x.(x+1)-5.(x+1).(x-2)=0
b)(4x+1).(x-2)-(2x-3)2=4
a)5(x+1)(x-x-2)=0
=>5(x+1).-2=0
=>5(x+1)=0
=>x+1=0
=>x=-1
a)5x.(x+1)-5.(x+1).(x-2)=0
⇒5x(x+1)-(5x-10)(x+1)=0
⇒(x+1)(5x-5x+10)=0
⇒10(x+1)=0
⇒x+1=0⇒x=-1
a) \(5x\left(x+1\right)-5\left(x+1\right)\left(x-2\right)=0\)
\(\Leftrightarrow5\left(x+1\right)\left(x-x+2\right)=0\)
\(\Leftrightarrow10\left(x+1\right)=0\)
\(\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
b) \(\left(4x+1\right)\left(x-2\right)-\left(2x-3\right)^2=4\)
\(\Leftrightarrow4x^2-7x-2-4x^2+12x-9=4\)
\(\Leftrightarrow5x=15\Leftrightarrow x=3\)
2. Tìm x biết:
a) 14,58 - x= -3,72
b) 3/4 + 1/2.x= -5/6
`a) 14,58 - x= -3,72`
`=> x= 14,58 - ( -3,72)`
`=> x= 14,58+ 3,72`
`=>x=18,3`
`b)3/4 + 1/2.x= -5/6`
`=> 1/2.x= -5/6-3/4`
`=> 1/2.x= -19/12``=>x=-19/12 : 1/2``=>x=-19/12xx2``=>x= -19/6`\(a)14,58-x=-3,72\\ x=14,58-\left(-3,72\right)\\ x=14,58+3,72\\ x=18,3\\ b)\dfrac{3}{4}+\dfrac{1}{2}.x=-\dfrac{5}{6}\\ \dfrac{1}{2}.x=-\dfrac{5}{6}-\dfrac{3}{4}\\ \dfrac{1}{2}.x=-\dfrac{19}{12}\\ x=-\dfrac{19}{12}:\dfrac{1}{2}\\ x=-\dfrac{19}{6}.\)
Tìm x,biết:
a)(5-x).(x-1)=-2x.(x-1)
b)(x+3)2-(x-13).(x+13)=0
a) \(\left(5-x\right)\left(x-1\right)=-2x\left(x-1\right)\)
\(\Rightarrow\left(5-x\right)\left(x-1\right)+2x\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(5-x+2x\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\)
b) \(\left(x+3\right)^2-\left(x-13\right)\left(x+13\right)=0\)
\(\Rightarrow x^2+6x+9-x^2+169=0\)
\(\Rightarrow6x=-178\Rightarrow x=-\dfrac{89}{3}\)