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15 tháng 4 2022

\(∘backwin\)

\(a ) ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) = 5750\)

\( ( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750 \)

\( 100 x + ( 1 + 100 ) ×100 : 2 = 5750\)

\(100 x + 5050 = 5750\)

\( 100 x = 5750 − 5050\)

\(100 x = 700\)

\(x = 700 : 100\)

\(x = 7\)

\(b,\) \(B=\)\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2021^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2020}+2021\)

\( B < 1 -\)\(\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2020}-\dfrac{1}{2021}\)

\(B<1-\)\(\dfrac{1}{2021}\)

\(B<\)\(\dfrac{2020}{2021}\)

\(\dfrac{2020}{2021}< 1\)

\(B<1\)

15 tháng 4 2022

a) (x+1) +(x+2 ) + ...+(x+100)=5750
= 100x + (1+2+3+...+100) = 5750
=100x + 5050 = 5750
--> 100x = 5750-5050=700
--> x=7

Cau1.Hay tinh hop li cac tong sau daya) A=1/3+1/3^2+1/3^3+....+1/3^100b)B=10/56+10/140+10/260+....+10/1400Cau2Cho C=2+2^2+2+3+...+2^99+2^100a)Tinh tong Cb)Tim x de2^2x-1-2=C        c)Chung minh rang C chia het ch 31Cau 3a) So sanh: A=2005^2005+1/2005^2006+1 va B=2005^2004+1/2005^2005+1b)Tim so nguyen m sao cho so m+6/m-1 la so nguyenCau4Cho AB=x(cm) AC=7(cm) BC=2x-1(cm) .Timx sao cho ba diem A B C  thang hangCau 5a) Tim x,y thuoc N biet 2^x+624=5^yb)Voi gia tri nao cua x ,y thi bieu thuc...
Đọc tiếp

Cau1.Hay tinh hop li cac tong sau day

a) A=1/3+1/3^2+1/3^3+....+1/3^100

b)B=10/56+10/140+10/260+....+10/1400

Cau2

Cho C=2+2^2+2+3+...+2^99+2^100

a)Tinh tong C

b)Tim x de2^2x-1-2=C        

c)Chung minh rang C chia het ch 31

Cau 3

a) So sanh: A=2005^2005+1/2005^2006+1 va B=2005^2004+1/2005^2005+1

b)Tim so nguyen m sao cho so m+6/m-1 la so nguyen

Cau4

Cho AB=x(cm) AC=7(cm) BC=2x-1(cm) .Timx sao cho ba diem A B C  thang hang

Cau 5

a) Tim x,y thuoc N biet 2^x+624=5^y

b)Voi gia tri nao cua x ,y thi bieu thuc A=/x-y/+/x+1/+2013 dat gia tri nho nhat .Tim gia tri nho nhat do

Chu y dau ''/'' la dau gia tri tuyet doi

Cau 6

De chuan bi cho ki thi hoc sinh gioi, mot hoc sinh giai 35 bai toan.Biet rang cu moi bai dat loai gioi duoc thuong 20 diem moi bai dat loai kha trung binh duoc thuong 5 diem . Con moi bai yeu, kem bi tru 10. Lam xong 35 bai em do duoc thuong 130 diem .Hoi co bao nhieu bai loai gioi ,bao nhieu bai loaiyeu ,kem .Biet rang co8 bai kha va trung binh

Ai lam dung minh tich cho

Nho giai ra nha

0
3 tháng 10 2017

Bài 1 câu g bạn kia làm sai mình sửa lại nhá

\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2\right)-12c^2\)

\(=3\left(a-b\right)^2-12c^2\)

\(=3\left[\left(a-b\right)^2-4c^2\right]\)

\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)

3 tháng 10 2017

Để mình làm tiếp cho :))

Bài 2 :

Câu a : \(37,5.8,5-7,5.3,4-6,6.7,5+1,5.37,5\)

\(=\left(37,5.8,5+1,5.37,5\right)-\left(7,5.3,4+6,6.7,5\right)\)

\(=37,5\left(8,5+1,5\right)-7,5\left(3,4+6,6\right)\)

\(=37,5.10-7,5.10\)

\(=10.30=300\)

Câu b : \(35^2+40^2-25^2+80.35\)

\(=\left(35^2+80.35+40^2\right)-25^2\)

\(=\left(30+45\right)^2-25^2\)

\(=75^2-25^2\)

\(=\left(75+25\right)\left(75-25\right)\)

\(=100.50=5000\)

Bài 3 :

Câu a : \(x^3-\dfrac{1}{9}x=0\)

\(\Leftrightarrow x\left(x^2-\dfrac{1}{9}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-\dfrac{1}{9}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\dfrac{1}{3}\end{matrix}\right.\)

Câu b : \(2x-2y-x^2+2xy-y^2=0\)

\(\Leftrightarrow2\left(x-y\right)-\left(x-y\right)^2=0\)

\(\Leftrightarrow\left(x-y\right)\left(2-x+y\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-y=0\\2-x+y=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=y\\x+y=2\Rightarrow x=2-y\end{matrix}\right.\)

Câu c :

\(x\left(x-3\right)+x-3=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)

\(x^2\left(x-3\right)+27-9x=0\)

\(\Leftrightarrow x^2\left(x-3\right)-9\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x^2-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x^2-9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=\pm3\end{matrix}\right.\)

Bài 4 :

Câu a :

\(x^2-4x+3\)

\(=x^2-x-3x+3\)

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

\(=x\left(x-1\right)-3\left(x-1\right)\)

\(=\left(x-1\right)\left(x-3\right)\)

Câu b :

\(x^2+x-6\)

\(=x^2-2x+3x-6\)

\(=x\left(x-2\right)+3\left(x-2\right)\)

\(=\left(x-2\right)\left(x+3\right)\)

Câu c :

\(x^2-5x+6\)

\(=x^2-2x-3x+6\)

\(=\left(x^2-2x\right)-\left(3x-6\right)\)

\(=x\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right)\left(x-3\right)\)

Câu d :

\(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-\left(2x\right)^2\)

\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)

Bài 1: 

a: \(P=\left(\dfrac{x-2}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+2}{\left(x+1\right)^2}\right)\cdot\dfrac{\left(x-1\right)^2\cdot\left(x+1\right)^2}{4}\)

\(=\dfrac{x^2-x-2-x^2-x+2}{\left(x-1\right)\left(x+1\right)^2}\cdot\dfrac{\left(x-1\right)^2\cdot\left(x+1\right)^2}{4}\)

\(=\dfrac{-2x}{1}\cdot\dfrac{x-1}{4}=-\dfrac{x\left(x-1\right)}{2}\)

b: Để \(\dfrac{P-4}{5}=x\) thì P-4=5x

=>P=5x+4

\(\Leftrightarrow-\dfrac{x\left(x-1\right)}{2}=5x+4\)

=>-x2+x=10x+8

=>x2-x=-10x-8

=>x2+9x+8=0

=>x=-8(nhận) hoặc x=-1(loại)

\(10A=\dfrac{10^{2021}+1+9}{10^{2021}+1}=1+\dfrac{9}{10^{2021}+1}\)

\(10B=\dfrac{10^{2022}+1+9}{10^{2022}+1}=1+\dfrac{9}{10^{2022}+1}\)

mà \(10^{2021}+1< 10^{2022}+1\)

nên A>B

15 tháng 10 2021

\(a,A=1+3+3^2+...+3^{125}\\ \Rightarrow3A=3+3^2+3^3+...+3^{126}\\ \Rightarrow2A=3^{126}-1\\ \Rightarrow A=\dfrac{3^{126}-1}{2}\\ c,2A=3^{2x}-1\\ \Rightarrow3^{126}-1=3^x-1\\ \Rightarrow x=126\)

\(d,A=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{124}+3^{125}\right)\\ A=\left(1+3\right)+3^2\left(1+3\right)+...+3^{124}\left(1+3\right)\\ A=\left(1+3\right)\left(1+3^2+...+3^{124}\right)\\ A=4\left(1+3^2+...+3^{124}\right)⋮4\)

16 tháng 10 2020

Chứng minh chia hết cho 31

C = 2 + 22 + 23 + ... + 299 + 2100

= ( 2 + 22 + 23 + 24 + 25 ) + ( 26 + 27 + 28 + 29 + 210 ) + ... + ( 296 + 297 + 298 + 299 + 2100 )

= 2( 1 + 2 + 22 + 23 + 24 ) + 26( 1 + 2 + 22 + 23 + 24 ) + ... + 296( 1 + 2 + 22 + 23 + 24 )

= 2.31 + 26.31 + ... + 296.31

= 31( 2 + 26 + ... +  296 ) chia hết cho 31 ( đpcm )

Tính tổng C

C = 2 + 22 + 23 + ... + 299 + 2100

=> 2C = 2( 2 + 22 + 23 + ... + 299 + 2100 )

           = 22 + 23 + ... + 2100 + 2101

=> C = 2C - C

         =  22 + 23 + ... + 2100 + 2101 - ( 2 + 22 + 23 + ... + 299 + 2100 )

         =  22 + 23 + ... + 2100 + 2101 - 2 - 22 - 23 - ... - 299 - 2100 

         = 2101 - 2

Tìm x để 22x-1 - 2 = C

22x-1 - 2 = C

<=> 22x-1 - 2 = 2101 - 2

<=> 22x-1 = 2101

<=> 2x - 1 = 101

<=> 2x = 102

<=> x = 51

11 tháng 4 2016
giup mik vs. Cau nao cux dk
29 tháng 6 2019

cmr bieu thuc sau luon luon co gia tri duong voi moi gia tri cua bien: 3x^2 -5x+3