Lời giải:
$(x-5)^{x+1}-(x-5)^{x+13}=0$
$\Leftrightarrow (x-5)^{x+1}[1-(x-5)^{12}]=0$
\(\Rightarrow \left[\begin{matrix} (x-5)^{x+1}=0\\ 1-(x-5)^{12}=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x-5=0\\ x-5=\pm 1\end{matrix}\right.\)
\(\Rightarrow \left[\begin{matrix} x=5\\ x=6\\ x=4\end{matrix}\right.\)
tìm x biết :
\(\left|x-1\right|+2.\left|x-2\right|+3.\left|x-3\right|+4.\left|x-4\right|+5.\left|x-5\right|+20x=0\)
Tìm x biết: \(\left(x-5\right)^{x+3}-\left(x-5\right)^{x+13}=0\)
Tìm x biết :
\(\left(x^2-20\right)\left(x^2-15\right)\left(x^2-10\right)\left(x^2-5\right)< 0\)
a) Tìm tập hợp các số nguyên x, biết rằng\(4\dfrac{5}{9}:2\dfrac{5}{18}-7< x< \left(3\dfrac{1}{5}:3,2+4,5.1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\)
b) tìm x, biết \(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{6}\right|+\left|x+\dfrac{1}{12}\right|+\left|x+\dfrac{1}{20}\right|+....+\left|x+\dfrac{1}{110}\right|-11x\)
c)Tính gt biểu thức \(C=2x^3-5y^3+2015\) tại x,y thỏa mãn \(\left|x-1\right|+\left(y+2\right)^{20}=0\)
\(\dfrac{3}{\left(x-4\right).\left(x-7\right)}+\dfrac{6}{\left(x-7\right).\left(x-13\right)}+\dfrac{15}{\left(x-13\right).\left(x-28\right)}-\dfrac{1}{x-28}=\dfrac{-5}{2}\)
Tìm x, y, zϵ R biết: \(\left(4x^2-4x+1\right)^{2022}+\left(y^2-\dfrac{4}{5}y+\dfrac{4}{25}\right)^{2022}+\left|x+y-z\right|=0\)
Tìm x, biết:
1) \(\left|4x\right|=3x+12\) 7) \(\left|5x\right|-3x-2=0\)
2) \(\left|2x+4\right|=2x-5\) 8) \(x-5x+\left|-2x\right|-3=0\)
3)\(\left|x+3\right|=3x-1\) 9) \(\left|3-x\right|+x^2-\left(4+x\right)x=0\)
4) \(\left|x-4\right|+3x=5\)
5)\(\left|x-5\right|=3x\)
6) \(\left|x+2\right|=2x-10\)
tìm x biết
a, \(3\left(x-2\right)-4\left(2x+1\right)-5\left(2x+3\right)=50\)
b, \(\left(x-7\right)^5-\left(x-7\right)^3=0\)
1) Cho đa thức \(f\left(x\right)=x^{14}-14.x^{13}+14.x^{12}-...+13.x^2-14.x+14\) Tính f(13)
2) Tính : \(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)...\left(\dfrac{3^{2000}}{2003}-81\right)\)