B1: cho đa thức M= -2024x²⁰²³ - 2y - 1/2x³y² - 10 + 2024x²⁰²³ + y - 1 Tính giá trị của đa thức M tại x = -2;y=-1
\(M=-2024x^{2023}-2y-\dfrac{1}{2}x^3y^2-10+2021^{2023}+y-1\)
\(M=\left(-2024x^{2023}+2024x^{2023}\right)-\left(2y-y\right)-\left(10+1\right)-\dfrac{1}{2}x^3y^2\)
\(M=-y-11-\dfrac{1}{2}x^3y^2\)
Thay x=-2, y=-1 vào M ta có:
\(M=-\left(-1\right)-11-\dfrac{1}{2}\cdot\left(-2\right)^3\cdot\left(-1\right)^2=-6\)
giai phuong trinh 1/(2008x+1)-1/(2009x+2)=1/(2010x+4)-1/(1011x+5)
\(\left|x+1\right|+\left|x+2\right|+....+\left|x+101\right|=2024x\)
\(\left|x+1\right|+\left|x+2\right|+.........+\left|x+101\right|=2024x\)
\(\Leftrightarrow\left|101x+\dfrac{\left[\left(101-1\right):1+1\right]\left(101+1\right)}{2}\right|=2024x\)
\(\Leftrightarrow\left|101x+5151\right|=2024x\)
\(\Leftrightarrow\left|101x+5151\right|-2024x=0\)
\(\Leftrightarrow-1923x+5151=0\)
\(\Leftrightarrow-1923x=5151\)
\(\Leftrightarrow x=\dfrac{5151}{-1923}\)
Vậy ..
đề mình ko ghi lại nhé
\(\Rightarrow\left|101x+\dfrac{\left[\left(101-1\right):1+1\right]\left(101+1\right)}{2}\right|=2024x\)
\(\Rightarrow\left|101x+5151\right|=2024x\)
\(\Rightarrow-1923+5151=0\)
\(\Rightarrow-1923x=5151\Rightarrow x=\dfrac{5151}{-1923}\)
\(\left|x+1\right|+\left|x+2\right|+...+\left|x+101\right|=2014x\)
Ta có:
\(\left|101x+\dfrac{\left[\left(101\right):1+1\right]\left(101+1\right)}{2}\right|=2024x\)
Từ đó \(\Rightarrow\left|101x+5151\right|=2024x\)
\(\Leftrightarrow\left|101x+5151\right|-2024x=0\)
\(\Leftrightarrow-1923x+5151=0\)
\(\Leftrightarrow-1923x=5151\)
\(\Rightarrow x=\dfrac{5151}{-1923}\)
Cho 2 số thực x,y thỏa mãn 6x^2+y(y+2x)=9xy và 3x>y>0.Tính P=xy/2024x^2-y^2
giải phương trình ngiệm nguyên x^5 + 2024x = 5^y + 1
Cho A= 1011x 1013 x.....x 2011. B = 1012 x 1014 x......x 2012. Tìm chữ số tận cùng của A + B
Chứng minh rằng:
a) A=1/3+1/(3^2)+1/(3^3)+...+1/(3^99)<1/2
b) B=3/(1^2*2^2)+5/(2^2*3^2)+7/(3^2*4^2)+...+19/(9^2*10^2)<1
c) C=1/3+2/(3^2)+3/(3^3)+4/(3^4)+...+100/(3^100)<3/4
a, Cho biết: \(1^2+2^2+3^2+...+10^2=385\)
Tính A= \(3^2+6^2+9^2+...+30^2\)
b, Cho biết: \(1^3+2^3+3^3+...+10^3=3025\)
Tính B= \(2^3+4^3+6^3+...+20^3\)
a: A=3^2(1^2+2^2+...+10^2)
=9*385
=3465
b: B=2^3(1^3+2^3+...+10^3)
=8*3025
=24200
Ngu như con chó thế. Mỗi bài cỏn con này mà ko giải được! ngu vãi lồn. Đúng là cha mẹ nuôi ăn tốn cơm, tốn gạo
A= 2+2^2+2^3+...+2^19+2^20
b=2+2^3+2^5+...2^97+2^99
C=5+5^2+5^3+...+5^50
D=1+3+3^2+3^3+...+3^100
\(2A-A=\left(2^2+2^3+...+2^{21}\right)-\left(2+2^2+...+2^{20}\right)\)
\(A=2^{21}-2\)
B tương tự câu A
\(5C-C=\left(5^2+5^3+...+5^{51}\right)-\left(5+5^2+...+5^{50}\right)\)
\(C=\dfrac{5^{51}-5}{4}\)
\(3D-D=3+3^2+...+3^{101}-\left(1+3+...+3^{100}\right)\)
\(D=\dfrac{3^{101}-1}{2}\)
\(A=2^1+2^2+2^3+...+2^{20}\)
\(2\cdot A=2^2+2^3+2^4+...+2^{21}\)
\(A=2^{21}-2\)
\(B=2^1+2^3+2^5+...+2^{99}\)
\(4\cdot B=2^3+2^5+2^7+...+2^{101}\)
\(B=\)\(\left(2^{101}-2\right):3\)
\(C=5^1+5^2+5^3+...+5^{50}\)
\(5\cdot C=5^2+5^3+5^4+...+5^{51}\)
\(C=(5^{51}-5):4\)
\(D=3^0+3^1+3^2+...+3^{100}\)
\(3\cdot D=3^1+3^2+3^3+...+3^{101}\)
\(D=(3^{101}-1):2\)
Rút gọn thành một lũy thừa
a) \(2^5\) . \(2^7\)
b) \(2^3\) . \(2^2\)
c) \(2^4\) . \(2^3\) . \(2^5\)
d) \(2^2\) . \(2^4\) . \(2^6\) . \(2\)
e) \(2\) . \(2^3\) . \(2^7\) . \(2^4\)
f) \(3^8\) . \(3^7\)
g) \(3^2\) . \(3\)
h) \(3^4\) . \(3^2\) . \(3\)
i) \(3\) . \(3^5\) . \(3^4\) . \(3^2\)
nhanh, giải chi tiết thì tớ tick cho
a) \(2^5\cdot2^7\)
\(=2^{5+7}\)
\(=2^{12}\)
b) \(2^3\cdot2^2\)
\(=2^{3+2}\)
\(=2^5\)
c) \(2^4\cdot2^3\cdot2^5\)
\(=2^{4+3+5}\)
\(=2^{12}\)
d) \(2^2\cdot2^4\cdot2^6\cdot2\)
\(=2^{2+4+6+1}\)
\(=2^{13}\)
e) \(2\cdot2^3\cdot2^7\cdot2^4\)
\(=2^{1+3+7+4}\)
\(=2^{15}\)
f) \(3^8\cdot3^7\)
\(=3^{8+7}\)
\(=3^{15}\)
g) \(3^2\cdot3\)
\(=3^{2+1}\)
\(=3^3\)
h) \(3^4\cdot3^2\cdot3\)
\(=3^{4+2+1}\)
\(=3^7\)
I) \(3\cdot3^5\cdot3^4\cdot3^2\)
\(=3^{1+5+4+2}\)
\(=3^{12}\)