Bài 1:
a. \(\left(5-x\right)^2+\left(5-x\right)^5=0\)
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b. (2:x+1)^2x=5^2x
\(\Rightarrow\)2:x+1=5
2:x =5-1
2:x =4
x =2:4
x =1/2
a. \(5^{4-x}+1=26\)
\(\Leftrightarrow5^{4-x}=26-1=25\)
\(\Leftrightarrow5^{4-x}=5^2\)
\(\Leftrightarrow4-x=2\)
\(\Leftrightarrow x=2\)
b. \(\left(\frac{2}{x}+1\right)^{2x}=5^{2x}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{2}{x}+1=5\\\frac{2}{x}+1=-5\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{2}{x}=4\\\frac{2}{x}=-6\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{3}\end{cases}}\)
c. \(\left(1-2x\right)^4-\left(1-2x\right)^6=0\)
\(\Leftrightarrow\left(1-2x\right)^4.\left[1-\left(1-2x\right)^2\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(1-2x\right)^4=0\\1-\left(1-2x\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}1-2x=0\\\left(1-2x\right)^2=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=1\\2x=0hoac2x=-2\end{cases}}\)
\(\Leftrightarrow x=\frac{1}{2},x=0,x=-1\)
\(B=\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\)
\(-5B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}\)
\(-5B-B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}-\)\(\left[\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\right]\)
\(-6B=\left(-5\right)^0-\left(-5\right)^{2018}\)
\(B=\left(5^{2018}-1\right):6\)
a)\(f\left(-1\right)=\left(-1\right)^2+5\cdot\left(-1\right)=1+\left(-5\right)=-4\)
\(f\left(-2\right)=\left(-2\right)^2+5\cdot\left(-2\right)=4+\left(-10\right)=-6\)
\(f\left(0\right)=0^2+5\cdot0=0\)
b)\(f\left(x\right)=-6\Leftrightarrow x^2+5x=-6\)
\(x^2+5x-\left(-6\right)=0\)
\(x^2+5x+6=0\)
\(x^2+2x+3x+6=0\)
\(x\left(x+2\right)+3\left(x+2\right)=0\)
\(\left(x+2\right)\left(x+3\right)=0\)
\(\Rightarrow x+2=0\) hoặc x+3=0
\(\Rightarrow\)x=-2 hoặc -3
a) f(-1) = (-1)2 + 5(-1) = -4 =y
tuong tu
b) x2 + 5x = -6
x2 +5x +6 = 0 => x2 +3x +2x +6 = 0
(x+3)(x+2) = 0
x = -3; x = -2
( chiều yên tâm đi học r)
minh co gang lam tung buoc nho cho ban hieu.
\(4-\left(x-\frac{1}{2}\right)-3\left(5-x\right)=0\)
{nhan pp pha ngoac
\(4-x+\frac{1}{2}-3.5+3.x=0\)
{gom cac so hang, hang so chuyen ben tay phai}
\(\left(3x-x\right)=3.5-4-\frac{1}{2}=15-4-\frac{1}{2}=11-\frac{1}{2}=\frac{21}{2}\)
\(2x=\frac{21}{2}\Rightarrow x=\frac{21}{2}:\frac{2}{1}=\frac{21}{2}.\frac{1}{2}=\frac{21}{4}\)
\(x=\frac{21}{4}\)
\(\left(2x+\frac{3}{5}\right)^2-\frac{9}{25}=0\)
\(\Leftrightarrow\left(2x+\frac{3}{5}\right)^2=\frac{9}{25}\)
\(\Leftrightarrow\left(2x+\frac{3}{5}\right)^2=\left(\frac{3}{5}\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}2x+\frac{3}{5}=\frac{3}{5}\\2x+\frac{3}{5}=-\frac{3}{5}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=0\\2x=-\frac{6}{5}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\frac{3}{5}\end{cases}}\)
_Tần vũ_
\(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)
\(\Leftrightarrow3\left(3x-\frac{1}{2}\right)^3=-\frac{1}{9}\)
\(\Leftrightarrow\left(3x-\frac{1}{2}\right)^3=-\frac{1}{27}\)
\(\Leftrightarrow\left(3x-\frac{1}{2}\right)^3=\left(-\frac{1}{3}\right)^3\)
\(\Leftrightarrow3x-\frac{1}{2}=\frac{-1}{3}\)
\(\Leftrightarrow3x=\frac{1}{6}\)
\(\Leftrightarrow x=\frac{1}{18}\)
_Tần Vũ_
a) => 4x + 2/3 = 0 hoặc 2/3x - 1 =0
4x= -2/3 hoặc 2/3x= 1
x = -2/3 . 1/4 hoặc x = 1.3/2
x = -1/6 hoặc x = 3/2
b) x+2 / x -1 = 5/2
=> 2(x+2) = 5(x-1)
2x + 4 = 5x - 5
5x - 2x= 4+5
3x = 9
=> x= 3
a) (4x+\(\frac{2}{3}\)) . ( \(\frac{2}{3}\)x-1)=0
\(\Rightarrow\)\(\orbr{\begin{cases}4x+\frac{2}{3}=0\\\frac{2}{3}x-1=0\end{cases}}\)
\(\Rightarrow\)\(\orbr{\begin{cases}x=\\x=\end{cases}}\)........
Tới đây bn tự giải nha
\(\left(5-x\right)^2+\left(5-x\right)^5=0\)
\(\Leftrightarrow\left(5-x\right)^2.\left[1+\left(5-x\right)^3\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(5-x\right)^2=0\\1+\left(5-x\right)^3=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}5-x=0\\\left(5-x\right)^3=-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=5\\5-x=-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=5\\x=6\end{cases}}\)
Vậy \(x\in\left\{5,6\right\}\)