Question

Giải pt:

a) x⁵ + x² + 2x + 2 = 0

b) x⁴ = 4x - 3

Answer 1

a (x+1)(x2-2x+2)(x2+x+1)=0

b (x-1)2(x2+2x+3)=0

...

Answer 2

a)\(x^5+x^2+2x+2=0\Leftrightarrow x^2\left(x^3+1\right)+2\left(x+1\right)=0\)

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

\(\Leftrightarrow\left(x+1\right)\left(x^4-x^3+x^2+2\right)=0\)

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

vậy...

b)\(x^4=4x-3\Leftrightarrow x^4-4x+3=0\)

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

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

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

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

mà x²+2x+3=(x+1)²+2>0 vs mọi x=> x=1

vậy....