#)Giải :
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Leftrightarrow\left(x-5\right)^4-\left(x-5\right)^6=0\)
\(\Leftrightarrow x-5=0\)
\(\Leftrightarrow x=5\)
\(\Leftrightarrow\left(x-5\right)^6-\left(x-5\right)^4=0\)
\(\Leftrightarrow\left(x-5\right)^4.\left[\left(x-5\right)^2-1\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2-1=0\end{cases}}\)
\(\Leftrightarrow\)x=5 hoặc x=6 hoặc x=4
(x-5)^4 = (x-5)^6
Gọi (x-5) là y ta có:
y^4 = y^6
=> để y^4 = y^6 thì chỉ khi y =-1 ; y=1 ; y=0
=> x=4 ; x=5 ; x=6
https://hotavn.ga/horobot/horobotmath.php?s=Tra+t%C6%B0%CC%80&val=(%20x%20-%205%20)%5E4%20%3D%20(%20x%20-%205%20)%5E6
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Leftrightarrow\left(x-5\right)^4-\left(x-5\right)^6=0\)
\(\Leftrightarrow x-5=0\)
\(\Leftrightarrow x=5\)
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Rightarrow\left(x-5\right)^4-\left(x-5\right)^6=0\)
\(\Rightarrow\left(x-5\right)^4\left[1-\left(x-5\right)^2\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\1-\left(x-5\right)^2=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=5\\x-5=\pm1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=5\\x=6\text{ }or\text{ }4\end{cases}}\)
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Rightarrow\left[\left(x-5\right)^2\right]^2=\left[\left(x-5\right)^3\right]^2\)
\(\Rightarrow\left(x-5\right)^2=\left(x-5\right)^3\)
\(\Rightarrow x^2-10x+25=x^3-15x^2+75x-125\)
\(\Rightarrow-x^3+16x^2-85x+150=0\)
\(\Rightarrow\left(-x^3+6x^2\right)+\left(10x^2-60x\right)-\left(25x-150\right)=0\)
\(\Rightarrow-x^2\left(x-6\right)+10x\left(x-6\right)-25\left(x-6\right)=0\)
\(\Rightarrow\left(x-6\right)\left(-x^2+10x-25\right)=0\)
\(\Rightarrow\left(x-6\right)\left[-\left(x^2-10x+25\right)\right]=0\)
\(\Rightarrow\left(x-6\right)\left[-\left(x-5\right)^2\right]=0\)
\(\Rightarrow\orbr{\begin{cases}x-6=0\\x-5=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=6\\x=5\end{cases}}\)
Vậy x=6 hoặc x=5
#)Góp ý :
Giải dễ hiểu hơn :v
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Leftrightarrow\left(x-5\right)^4-\left(x-5\right)^6=0\)
\(\Leftrightarrow\left(x-5\right)^4\left[1-\left(x-5\right)^2\right]=0\)
\(\Leftrightarrow\left(x-5\right)^4\left(1-x+5\right)\left(1+x-5\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(x-5\right)^4=0\\6-x=0\\x-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=5\\x=6\\x=4\end{cases}}}\)
Vậy ...
P/s : Vì cái [ k có chỗ cho đủ 3 biểu thức nên mk dùng { nha, đừng ai hiểu nhầm :v
( x - 5 )4 = ( x - 5 )6
=> ( x - 5 )6 - ( x - 5 )4 = 0
=> ( x - 5 )4. [ ( x - 5 ) 2 - 1 ] = 0
=> ( x - 5 )4 = 0 hoặc [ ( x - 5 ) 2 - 1 ] = 0
='> x - 5 = 0 hoặc ( x - 5 )2 = 1
=> x - 5 = 0 hoặc x - 5 = 1 hoặc x - 5 = -1
Vậy x = { 4 ; 5 ; 6 }
