Question

tìm x
n, (x+1/x) ² - 3(x+1/x)+2=0
o, 9=(x-1)x(x+1)(x+2) - 24=0
p, x^4 - 4x ³ + 6x ² - 4x +1=0

Answer 1

n: ĐKXĐ: x<>0

\(\left(x+\dfrac{1}{x}\right)^2-3\left(x+\dfrac{1}{x}\right)+2=0\)

=>\(\left(x+\dfrac{1}{x}\right)^2-2\left(x+\dfrac{1}{x}\right)-\left(x+\dfrac{1}{x}\right)+2=0\)

=>\(\left(x+\dfrac{1}{x}-2\right)\left(x+\dfrac{1}{x}-1\right)=0\)

=>\(\dfrac{x^2+1-2x}{x}\cdot\dfrac{x^2+1-x}{x}=0\)

=>\(\left(x^2-2x+1\right)\left(x^2-x+1\right)=0\)

=>\(\left(x-1\right)^2\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\right]=0\)

=>\(\left(x-1\right)^2=0\)

=>x-1=0

=>x=1

p: \(x^4-4x^3+6x^2-4x+1=0\)

=>\(x^4-x^3-3x^3+3x^2+3x^2-3x-x+1=0\)

=>\(x^3\left(x-1\right)-3x^2\left(x-1\right)+3x\left(x-1\right)-\left(x-1\right)=0\)

=>\(\left(x-1\right)\left(x^3-3x^2+3x-1\right)=0\)

=>\(\left(x-1\right)^4=0\)

=>x-1=0

=>x=1