Bài 3: Ghi số tự nhiên

Do 12 > 11

⇒ 12/13 > 11/13 (1)

Do 13 < 14

⇒ 11/13 > 11/14 (2)

Từ (1) và (2) ⇒ 12/13 > 11/14

Lời giải:

$A=1+2-3-4+5+6-7-8+9+10-11-12+....+993+994-995-996+997+998$

$=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+...+(993+994-995-996)+(997+998)$

$=(-4)+(-4)+(-4)+....+(-4)+1995$

Số lần xuất hiện của $-4$ là:

$[(996-1):1+1]:4=249$

$A=(-4).249+1995=999$

c: (x-5)(x-7)=0

=>\(\left[{}\begin{matrix}x-5=0\\x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=7\end{matrix}\right.\)

\(a,x^2=64\\ \Rightarrow x^2=8^2\\ \Rightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

\(b,\left(x-2\right)^2=16\\ \Rightarrow\left(x-2\right)^2=4^2\\ \Rightarrow\left[{}\begin{matrix}x-2=4\\x-2=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=6\\x=-2\end{matrix}\right.\\ c,\left(2x-3\right)^2=9\\ \Rightarrow\left(2x-3\right)^2=3^2\\ \Rightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)

`g, 2x+5=3^4:3^2`

`=> 2x+5= 3^2`

`=>2x+5=9`

`=> 2x=9-5`

`=>2x=4`

`=>x=4:2`

`=>x=2`

`h, (3x-2^4) .7^3 =2.7^4`

`=> 3x-16 =2. 7^4 : 7^3`

`=> 3x-16 = 2. 7`

`=> 3x-16=14`

`=> 3x=14+16`

`=>3x=30`

`=>x=30:3`

`=>x=10`

\(a,x^2=64\)

\(\Rightarrow x^2=\left(\pm8\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

\(---\)

\(b,\left(x-2\right)^2=16\)

\(\Rightarrow\left(x-2\right)^2=\left(\pm4\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x-2=4\\x-2=-4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6\\x=-2\end{matrix}\right.\)

\(---\)

\(c,\left(2x-3\right)^2=9\)

\(\Rightarrow\left(2x-3\right)^2=\left(\pm3\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=3+3\\2x=-3+3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6:2=3\\x=0\end{matrix}\right.\)

\(---\)

\(g,2x+5=3^4:3^2\)

\(\Rightarrow2x+5=3^2\)

\(\Rightarrow2x+5=9\)

\(\Rightarrow2x=9-5\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=4:2=2\)

\(---\)

\(h,\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)

\(\Rightarrow3x-2^4=\dfrac{2\cdot7^4}{7^3}\)

\(\Rightarrow3x-16=2\cdot7\)

\(\Rightarrow3x-16=14\)

\(\Rightarrow3x=14+16\)

\(\Rightarrow3x=30\)

\(\Rightarrow x=30:3=10\)

#\(Toru\)

`x-23=67`

`=>x=67+23`

`=>x=90`

Vậy `x=90`

__

`57 +7x=120`

`=> 7x=120-57`

`=>7x=63`

`=>x=63:7`

`=>x=9`

vậy `x=9`

__

`38-2x=14`

`=>2x=38-14`

`=>2x=  24`

`=>x=24:2`

`=>x=12`

__

`140:(x-8)=7`

`=> x-8=140:7`

`=>x-8=20`

`=>x=20+8`

`=>x=28`

__

`(2+x):5=6`

`=>2+x=6xx5`

`=>2+x=30`

`=>x=30-2`

`=>x=28`

Vậy `x=28`

__

`2(x-51)=24`

`=>x-51=24:2`

`=>x-51= 12`

`=>x=12+51`

`=>x=63`

Vậy `x=63`

\(a)x-23=67\\\Rightarrow x=67+23\\\Rightarrow x=90\\---\\b)57+7x=120\\\Rightarrow 7x=120-57\\\Rightarrow7x=63\\\Rightarrow x=63:7\\\Rightarrow x=9\\---\\c)38-2x=14\\\Rightarrow 2x=38-14\\\Rightarrow 2x=24\\\Rightarrow x=24:2\\\Rightarrow x=12\\---\)

\(f)140:(x-8)=7\\\Rightarrow x-8=140:7\\\Rightarrow x-8=20\\\Rightarrow x=20+8\\\Rightarrow x=28\\---\\g)(2+x):5=6\\\Rightarrow 2+x=6\cdot5\\\Rightarrow 2+x=30\\\Rightarrow x=30-2\\\Rightarrow x=28\)

#\(Toru\)

Lời giải:

Gọi số tự nhiên cần tìm là $a$. Theo bài ra ta có:

$a=12.17+r$ với $r$ là số dư, $r< 12$

$a=204+r$

Vì $a$ chia $60$ dư $31$ nên $a-31\vdots 60$

$\Rightarrow 204+r-31\vdots 60$

$\Rightarrow r+173\vdots 60$

$\Rightarrow r+180-7\vdots 60$

$\Rightarrow r-7\vdots 60$

Mà $r$ là stn nhỏ hơn 12 nên $r=7$ là đáp án duy nhất thỏa mãn.

Khi đó: $a=204+r=204+7=211$

\(x^2+xy+x+y=1\)

\(\Rightarrow x\left(x+y\right)+\left(x+y\right)=1\)

\(\Rightarrow\left(x+1\right)\left(x+y\right)=1\)

Nhưng x,y ϵ N nên:

\(x+1=1\)

\(\Rightarrow x=1-1\)

\(\Rightarrow x=0\)

\(x+y=1\)

\(\Rightarrow0+y=1\)

\(\Rightarrow y=1\)

Vậy: ...

\(x^2+xy+x+y=1\) \(\left(x;y\in N\right)\)

\(\Rightarrow x\left(x+y\right)+\left(x+y\right)=1\)

\(\Rightarrow\left(x+1\right)\left(x+y\right)=1\)

\(\Rightarrow\left(x+1\right);\left(x+y\right)\in U\left(1\right)=\left\{1\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(0;1\right)\right\}\)

3532 số liền trước là : 3531

3529 số liền sau là : 2530

tổng 2 số là: 3531+2530=6061

Các phần tử là:

\(14;25;36;47;58;69\)

Tập hợp A là:

\(A=\left\{14;25;36;47;58;69\right\}\)

A = {14; 25; 36; 47; 58; 69}

Số số hạng là (148-52):2+1=49(số)

Tổng là (148+52)*49/2

=49*100

=4900