\(100+200+800+500\times851+10000:100\)

\(=300+800+425500+100\)

\(=1100+425500+100\)

\(=1200+425500\)

\(=426700\)

100+200+800+500x851+10000:100= 100 + 200 + 800 +425500 + 100 = 426700

Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

=> 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

=> 2A - A = (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128) -                                     (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)

=> A = 1 - 1/256

=> A = 255/256

Vậy: ...

Mỗi hộp kẹo nặng:

384:12=32(g)

Đổi 12kg= 12000g

12kg kẹo chia vào được số hộp:

12000:32= 375(hộp)

Đ.số:375 hộp

dễ ẹt

4S=1.2.3.4+2.3.4.4+3.4.5.4+...+k(k+1)(k+2).4=

=1.2.3.4+2.3.4(5-1)+3.4.5.(6-2)+...+k(k+1)(k+2)[(k+3)-(k-1)]=

=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-...-(k-1)k(k+1)(k+2)+k(k+1)(k+2)(k+3)=

=k(k+1)(k+2)(k+3)=k(k+3)(k+1)(k+2)=

=(k²+3k)(k²+3k+2)=(k²+3k)²+2(k²+3k)

=> 4S+1=(k²+3k)²+2(k²+3k)+1=[(k²+3k)+1]²

\(100-10+9\times8:5\times10-8\)

\(=90+9\times\dfrac{8}{5}\times10-8\)

\(=82+\dfrac{9\times8\times10}{5}\)

\(=82+9\times8\times2\)

\(=82+144\)

\(=226\)

100- 10+ 9x8:5x 10- 8

=100- 10+ 72: 5x10-8

=100- 10+ 14,4x10 -8

= 100-10 + 144 -8

=90 + 144 -8

= 234 - 8

=226

.

Giúp trở lời đầy đủ

\(n^2+4n+2013=\left(n^2+4n+4\right)+2009=k^2\)

\(\Leftrightarrow\left(n+2\right)^2+2009=k^2\)

\(\Rightarrow\left(k-n-2\right)\left(k+n+2\right)=2009\)

\(\Rightarrow k-n-2\) và \(k+n+2\) là ước của 2009

Ta có các TH

\(\left\{{}\begin{matrix}k-n-2=-1\\k+n+2=-2009\end{matrix}\right.\) 

Hoặc

\(\left\{{}\begin{matrix}k-n-2=-2009\\k+n+2=-1\end{matrix}\right.\)

Hoặc

\(\left\{{}\begin{matrix}k-n-2=1\\k+n+2=2009\end{matrix}\right.\)

Hoặc

\(\left\{{}\begin{matrix}k-n-2=2009\\k+n+2=1\end{matrix}\right.\)

Giải các hệ trên tìm n

a) \(\left(2x-3\right)\left(2x+3\right)=0\)

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

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

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

b) \(\left(x-4\right)\left(x-1\right)\left(x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\\x-2=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=1\\x=2\end{matrix}\right.\)

c) \(2x\left(3x-1\right)-3x\left(5+2x\right)=0\)

\(\Rightarrow x\left[2\left(3x-1\right)-3\left(5+2x\right)\right]=0\)

\(\Rightarrow x\left(6x-2-15-6x\right)\)

\(\Rightarrow-16x=0\)

\(\Rightarrow x=0\)

d) \(\left(3x-2\right)\left(3x+2\right)-4\left(x-1\right)=0\)

\(\Rightarrow9x^2-4-4x+4=0\)

\(\Rightarrow9x^2-4x=0\)

\(\Rightarrow x\left(9x-4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\9x-4=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{9}\end{matrix}\right.\)

\(a,\left(2x-3\right)\left(2x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\\ b,\left(x-4\right)\left(x-1\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=1\\x=2\end{matrix}\right.\)

\(C=1^2+2^2+3^2+...+19^2+20^2\)

\(\Rightarrow C=\dfrac{20\left(20+1\right)\left(2.20+1\right)}{6}\)

\(\Rightarrow C=\dfrac{20.21.41}{6}=2870\)

C = 1² + 2² + 3²+....+ 19² + 20² (mới đúng, em xem lại đề bài)

2^x = 64

⇒ 2^x = 2⁶

⇒ x = 6.

7^x = 7¹⁰ : 7⁵

⇒ 7^x = 7⁵

⇒ x = 5.

3^x = 3¹⁵ : 243

⇒ 3^x = 3¹⁵ : 3⁵

⇒ 3^x = 3¹⁰

⇒ x = 10.

\(2^x=64=2^6\Rightarrow x=6\\ ---\\ 7^x=7^{10}:7^5=7^5\Rightarrow x=5\\ ----\\ 3^x=3^{15}:243=3^{15}:3^5=3^{10}\Rightarrow x=10\)