x =   0 khỏi tính cũng biết .

xⁿ - 2xⁿ⁺¹ + 5xⁿ - 4xⁿ⁺¹ = 0

=>xⁿ -2xⁿ +x +5xⁿ-4xⁿ+x=0

=> (xⁿ-2xⁿ+5xⁿ-4xⁿ)+(x+x)=0

=> 0+2x=0

=> x=0

vậy x=0

<=>5xⁿ.x²-3xⁿ+2xⁿ.x²-4xⁿ+xⁿ.x²-xⁿ=0

<=>(5xⁿ.x²+2xⁿ.x²)-(3xⁿ+4xⁿ)+(xⁿ.x²-xⁿ)=0

<=>7xⁿ.x²-7xⁿ+xⁿ(x²-1)=0

<=>7xⁿ(x²-1)+xⁿ(x²-1)=0

<=>8xⁿ(x²-1)=0<=>x²-1=0<=>x=-1 hoặc x=1

\(x^n-2x^{n+1}+5x^n-4x^{n+1}=0\)

\(\Rightarrow x^n-2x^n.2+5x^n-4x^n.2=0\)

\(\Rightarrow\left(x^n+5x^n\right)-\left(2x^n.2+4x^n.2\right)=0\)

\(\Rightarrow6x^n-2\left(2x^n+4x^n\right)=0\)

\(\Rightarrow6x^n-2.6x^n=0\)

\(\Rightarrow6x^n\left(1-2\right)=0\)

\(\Rightarrow6x^n=0\)

\(\Rightarrow x=0\)

Vậy x = 0

Bài 5.5:

\(\left(2x-3\right)\left(x+1\right)+\left(4x^3-6x^2-6x\right):\left(-2x\right)=18\)

\(\Leftrightarrow\left(2x^2+2x-3x-3\right)+2x\cdot\left(2x^2-3x-3\right):\left(-2x\right)=18\)

\(\Leftrightarrow2x^2-x-3-2x^2+3x+3=18\)

\(\Leftrightarrow2x=18\)

\(\Leftrightarrow x=\dfrac{18}{2}\)

\(\Leftrightarrow x=9\)