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\(\left(2x-15\right)^3=\left(2x-15\right)^5\\ \Rightarrow\left(2x-15\right)^2=1\\ \Rightarrow\left[{}\begin{matrix}2x-15=-1\\2x-15=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=7\\x=8\end{matrix}\right.\)
a) 2^x.2^4=128
=>2^x.2^2=2^7
=>2^x=2^7:2^2
=>2^x=2^5
=>x=5
b)x^15=x
=>x^15-x=0
=>x(x^16-x)=0
=>2 trượng hợp:x=0 và x^16-1=0(x^16-1=0 cx 2 th nha)
b),d),e) như nhau nha!
c) dễ rồi
\(a)2^x\cdot4=128\)
\(\Rightarrow2^x=\frac{128}{4}\)
\(\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
\(b)x^{15}=x\)
\(\Rightarrow x^{15}-x=0\)
\(\Rightarrow x(x^{14}-1)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=0\\x^{14}=1\end{cases}\Rightarrow}\hept{\begin{cases}x=0\\x=1\end{cases}}\)
\(c)(2x+1)^3=125\)
\(\Rightarrow(2x+1)^3=5^3\)
\(\Rightarrow2x+1=5\)
\(\Rightarrow2x=5-1\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=4:2=2\)
\(d)(x-5)^4=(x-5)^6\)
\(\Rightarrow(x-5)^6-(x-5)^4=0\)
\(\Rightarrow(x-5)^4\cdot\left[(x-5)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}(x-5)^4=0\\(x-5)^2-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=6\end{cases}}\)
\(e)(2x-15)^5=(2x-15)^3\)
\(\Rightarrow(2x-15)^5-(2x-15)^3=0\)
\(\Rightarrow(2x-15)^3-\left[(2x-15)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}(2x-15)^3=0\\(2x-15)^2-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\varnothing\\x=8\end{cases}}\)
Chúc bạn hoc tốt :>
a) \(3\left(4-2x\right)-2\left(x+3\right)=12-7x\)
\(\Leftrightarrow\)\(12-6x-2x-6=12-7x\)
\(\Leftrightarrow\)\(6-8x=12-7x\)
\(\Leftrightarrow\)\(x=-6\)
Vậy...
b) \(\left|16+\right|3\left(x-2\right)||-5=20\)
\(\Leftrightarrow\)\(\left|16+\right|3\left(x-2\right)||=25\)(1)
Ta thấy: \(\left|3\left(x-2\right)\right|\ge0\)\(\Rightarrow\)\(16+\left|3\left(x-2\right)\right|>0\)
nên từ (1) \(\Rightarrow\) \(16+\left|3\left(x-2\right)\right|=25\)
\(\Leftrightarrow\)\(\left|3\left(x-2\right)\right|=9\)
\(\Leftrightarrow\) \(\orbr{\begin{cases}3\left(x-2\right)=9\\3\left(x-2\right)=-9\end{cases}}\)
\(\Leftrightarrow\) \(\orbr{\begin{cases}x-2=3\\x-2=-3\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=5\\x=-1\end{cases}}\)
Vậy....
c) \(\left|-5-3^2\right|-||3x+5|-7.2^3|=3^9:3^7\)
\(\Leftrightarrow\)\(14-||3x+5|-56|=9\)
\(\Leftrightarrow\)\(||3x+5|-56|=5\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\left|3x+5\right|-56=5\\\left|3x+5\right|-56=-5\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\left|3x+5\right|=61\\\left|3x+5\right|=51\end{cases}}\)
đến đây bn giải tiếp nhé
\(3\left(2x-6\right)-4\left(1+2x\right)-2\left(x-4\right)=4-3\left(1+2x\right)-5\left(1-2x\right).\)
\(\Leftrightarrow6x-18-4-8x-2x+8=4-3-6x-5+10x\)
\(\Leftrightarrow-4x-14=4x-4\)
\(\Leftrightarrow-4x-4x=-4+14\)
\(\Leftrightarrow-8x=10\)
\(\Leftrightarrow x=-\frac{5}{4}\)
2a - (5- 4a) +(6a -1) -(2+a)
= -10a - 8a^2 +6a -1 -2 -a
= -8a^2 -5a -3
5a - 2b +3 - (2a -5b +6) +(a+3b -1)
= 5a -2b +3 -2a+5b -6 +a + 3b -1
= 4a +6b -4
6x(x-1) -1(6x^2 -8x +3) = 7 -(x-1)
6x^2 -6x - 6x^2 + 8x -3 = 7 -x +1
3x = 11
x= 11/3
7x(2x-1) - (14x^2 -8x +5) = 7- (-2x +3)
14x^2 - 7x - 14x^2 + 8x - 5 = 7 + 2x -3
-x = 9
x=-9
(2x - 15)⁵ = (2x - 15)³
(2x - 15)⁵ - (2x - 15)³ = 0
(2x - 15)³.[(2x - 15)² - 1] = 0
(2x - 15)³.[(2x - 15)(2x - 15) - 1] = 0
(2x - 15)³.(4x² - 30x - 30x + 225 - 1) = 0
(2x - 15)³.(4x² - 60x + 225 - 1) = 0
(2x - 15)³.(4x² - 60x + 224) = 0
4.(2x - 15)³.(x² - 15x + 56) = 0
4.(2x - 15)³.(x² - 7x - 8x + 56) = 0
4.(2x - 15)³.[(x² - 7x) - (8x - 56)] = 0
4.(2x - 15)³.[x(x - 7) - 8(x - 7)] = 0
4.(2x - 15)³.(x - 7)(x - 8) = 0
(2x - 15)³ = 0 hoặc x - 7 = 0 hoặc x - 8 = 0
*) (2x - 15)³ = 0
2x - 15 = 0
2x = 15
x = 15/2
*) x - 7 = 0
x = 7
*) x - 8 = 0
x = 8
Vậy x = 7; x = 15/2; x = 8
1 x 99 + 3 x 97+... + 49 x 51 cứu với