Câu hỏi của Nguyễn Thế Thành Long

Question

Bài 1:a. Tính: 1+22+23+....+29+210b. Tìm x biết:a] 60 - 3 . [x-1] = 23. 3b] [3x - 2]3 = 2 . 25 c] 5x+1 - 5x = 500d] x2 = x4

HT.Phong (9A5) · Accepted Answer

a) Đặt: $A=1+2^2+2^3+...+2^{10}$$\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)$$\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}$$\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)$$\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)$$\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)$$\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045$Vậy: $1+2^2+2^3+...+2^{10}=2045$b) a] $60-3\left(x-1\right)=2^3\cdot3$$\Rightarrow60-3\left(x-1\right)=24$$\Rightarrow3\left(x-1\right)=36$$\Rightarrow x-1=12$$\Rightarrow x=13$b] $\left(3x-2\right)^3=2\cdot2^5$$\Rightarrow\left(3x-2\right)^3=2^6$$\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3$$\Rightarrow3x-2=2^2$$\Rightarrow3x=6$$x=2$c] $5^{x+1}-5^x=500$$\Rightarrow5^x\left(5-1\right)=500$$\Rightarrow5^x\cdot4=500$$\Rightarrow5^x=125$$\Rightarrow5^x=5^3$$\Rightarrow x=3$d] $x^2=x^4$$\Rightarrow x=x^2$$\Rightarrow x-x^2=0$$\Rightarrow x\left(1-x\right)=0$$\Rightarrow\left[{}\begin{matrix}x=0\1-x=0\end{matrix}\right.$$\Rightarrow\left[{}\begin{matrix}x=0\x=1\end{matrix}\right.$Câu trả lời: a) Đặt: $A=1+2^2+2^3+...+2^{10}$$\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)$$\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}$$\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)$$\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)$$\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)$$\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045$Vậy: $1+2^2+2^3+...+2^{10}=2045$b) a] $60-3\left(x-1\right)=2^3\cdot3$$\Rightarrow60-3\left(x-1\right)=24$$\Rightarrow3\left(x-1\right)=36$$\Rightarrow x-1=12$$\Rightarrow x=13$b] $\left(3x-2\right)^3=2\cdot2^5$$\Rightarrow\left(3x-2\right)^3=2^6$$\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3$$\Rightarrow3x-2=2^2$$\Rightarrow3x=6$$x=2$c] $5^{x+1}-5^x=500$$\Rightarrow5^x\left(5-1\right)=500$$\Rightarrow5^x\cdot4=500$$\Rightarrow5^x=125$$\Rightarrow5^x=5^3$$\Rightarrow x=3$d] $x^2=x^4$$\Rightarrow x=x^2$$\Rightarrow x-x^2=0$$\Rightarrow x\left(1-x\right)=0$$\Rightarrow\left[{}\begin{matrix}x=0\1-x=0\end{matrix}\right.$$\Rightarrow\left[{}\begin{matrix}x=0\x=1\end{matrix}\right.$

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