Ôn tập toán 6

a) \(2x-13=7\)

\(\Leftrightarrow2x=7+13=20\)

\(\Leftrightarrow x=\frac{20}{2}=10\)

b) \(23-x=31-\left(-9\right)\)

\(\Leftrightarrow23-x=40\)

\(\Leftrightarrow x=23-40=-17\)

c) \(\left|x+13\right|-4=16\)

\(\Leftrightarrow\left|x+13\right|=16+4=20\)

\(\Leftrightarrow\left[\begin{matrix}x+13=20\Rightarrow x=7\\x+13=-20\Rightarrow x=-33\end{matrix}\right.\)

d) Vì 45 \(⋮x\) mà x > 15

\(\Rightarrow\) x = 45

a, 2x = 7 + 13 =20 => x = 20 : 2 =10

b, 23 - x = 31 + 9 = 40 => x = 23 - 40 = -17

c, x = 7 ; x = -33

d, x = 22,5

a, \(2x-13=7\)

\(2x=7+13\)

\(2x=20\)

\(x=\frac{20}{2}\)

\(x=10\)

b, \(23-x=31-\left(-9\right)\)

\(23-x=40\)

\(x=23-40\)

\(x=-17\)

c, \(\left|x+13\right|-4=16\)

\(\left|x+13\right|=16+4\)

\(\left|x+13\right|=20\)

\(\Rightarrow\left[\begin{matrix}x+13=20\\x+13=-20\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=7\\x=-33\end{matrix}\right.\)

d, \(45⋮x;x>15\)

Vì \(45⋮x\) nên x là Ư(45)

Mà \(Ư\left(45\right)=\left\{1;3;5;9;15;45\right\}\)

Vì x > 15 nên x = 45.

a) Để \(A=\dfrac{5}{\left(x-3\right)^2+1}\) đạt giá trị lớn nhất

\(\Leftrightarrow\left(x-3\right)^2+1\) phải nhỏ nhất

Mà \(\left(x-3\right)^2\ge0\Leftrightarrow\left(x-3\right)^2+1\ge1\)

\(\Rightarrow A_{max}=\dfrac{5}{\left(x-3\right)^2+1}=\dfrac{5}{1}=5\)

Dấu "=" xảy ra \(\Leftrightarrow\left(x-3\right)^2=0\Leftrightarrow x-3=0\Rightarrow x=3\)

Vậy \(A_{max}=5\) tại \(x=3\)

b) Để \(B=\dfrac{4}{\left|x-2\right|+2}\) đạt giá trị lớn nhất

\(\Leftrightarrow\left|x-2\right|+2\) phải nhỏ nhất

Mà \(\left|x-2\right|\ge0\Leftrightarrow\left|x-2\right|+2\ge2\)

\(\Rightarrow B_{max}=\dfrac{4}{\left|x-2\right|+2}=\dfrac{4}{2}=2\)

Dấu "=" xảy ra \(\Leftrightarrow\left|x-2\right|=0\Leftrightarrow x-2=0\Rightarrow x=2\)

Vậy \(B_{max}=2\) tại \(x=2\)

a, \(\left(1+3x\right)^3=64\Leftrightarrow\left(1+3x\right)^3=4^3\)

\(\Leftrightarrow1+3x=4\Leftrightarrow3x=3\Rightarrow x=1\in Z\)

Vậy x = 1

b, \(\left(11-4x\right)^3=343\Leftrightarrow\left(11-4x\right)^3=7^3\)

\(\Leftrightarrow11-4x=7\Rightarrow4x=11-7\Rightarrow4x=4\Rightarrow x=1\in Z\)

Vậy x = 1

1.

( 1 + 3x ) = 64

( 1 + 3x ) = 4³

( 1 + 3x ) = 4

3x = 4 - 1

3x = 3

x = 3 : 3

x = 1

2.

( 11 - 4x )³ = 343

( 11 - 4x )³ = 7³

( 11 - 4x ) = 7

4x = 11 - 7

4x = 4

x = 4 : 4

x = 1

\(-5\left(x+\dfrac{1}{2}\right)-\dfrac{1}{2}\left(x-\dfrac{2}{3}\right)=\dfrac{3}{2}x-\dfrac{5}{6}\)

\(-5x-\dfrac{5}{2}-\dfrac{1}{2}x+\dfrac{1}{3}=\dfrac{3}{2}x-\dfrac{5}{6}\)

\(-\dfrac{11}{2}x\)\(-\dfrac{5}{2}\)\(=\dfrac{3}{2}x-\dfrac{5}{6}\)

\(-\dfrac{11}{2}x:\dfrac{3}{2}x=-\dfrac{5}{6}+\dfrac{5}{2}\)

\(-\dfrac{11}{3}x=\)\(\dfrac{5}{3}\)

\(x=\dfrac{5}{11}\)

\(\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+...............+\dfrac{2}{2008.2009}\)

\(=2\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+................+\dfrac{1}{2008.2009}\right)\)

\(=2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.................+\dfrac{1}{2008}-\dfrac{1}{2009}\right)\)

\(=2\left(1-\dfrac{1}{2009}\right)\)

\(=2.\dfrac{2008}{2009}=\dfrac{4016}{2009}\)

Bài 1 : Tìm y

Để \(\dfrac{1}{3}\) . Y + \(\dfrac{2}{5}\) ( x-1 ) =0

=> \(\dfrac{1}{3}\). Y và \(\dfrac{2}{5}\)(x-1) \(\ge\) 0

\(\dfrac{1}{3}\) . Y + \(\dfrac{2}{5}\) ( x-1 ) =0

=> \(\dfrac{1}{3}\) . Y = 0 => y = 0

=> \(\dfrac{2}{5}\) ( x - 1 ) = 0 => x = 1

Vậy : Y = 0

\(\dfrac{1}{3}\cdot y\) + \(\dfrac{2}{5}\cdot\left(x-1\right)\) = 0

Xét TH1 : x;y \(\in\)N

Suy ra \(\left\{{}\begin{matrix}\dfrac{1}{3}\cdot y=0\\\dfrac{2}{5}\cdot\left(x-1\right)=0\end{matrix}\right.\)

Suy ra y = 0

Xét TH2 : x;y \(\in\) R

Ngoại trừ nghiệm ở TH1 suy ra 1/3 x Y và 2/5 x ( x - 1 ) là hai số đối nhau

Vậy có vô hạn nghiệm của y

so sánh hai số này à

UK

a: Đề sai rồi bạn

b: \(\dfrac{\left(1.16-x\right)\cdot5.25}{\left(10+\dfrac{5}{9}-7-\dfrac{1}{4}\right)\cdot\dfrac{36}{17}}=\dfrac{3}{4}\)

\(\Leftrightarrow21\left(1.16-x\right)=3\cdot\dfrac{36}{17}\cdot\left(3+\dfrac{5}{9}-\dfrac{1}{4}\right)\)

\(\Leftrightarrow21\left(1.16-x\right)=\dfrac{108}{17}\cdot\dfrac{108+20-9}{36}\)

\(\Leftrightarrow21\cdot\left(1.16-x\right)=21\)

=>1,16-x=1

hay x=0,16