Phương trình x^4=x có bao nhiêu nghiệm?

2 câu trả lời

Đáp án: 2

 

Giải thích các bước giải:

${{x}^{4}}-x=0$

$\Leftrightarrow x\left( {{x}^{3}}-1 \right)=0$

$\Leftrightarrow x=0$ hoặc ${{x}^{3}}=1$

$\Leftrightarrow x=0$ hoặc $x=1$

Vậy có 2 nghiệm

Đáp án:

 `2`

Giải thích các bước giải:

`x^4=x`

`<=> x^4-x=0`

`<=> x(x^3-1)=0`

`<=> x(x-1)(x^2+x+1)=0`

Mà `x^2+x+1=(x+1/2)^2+ 3/4 >=3/4 >0 \forall x`

Nên `[(x=0),(x-1=0):}`

`<=> [(x=0),(x=1):}`

Vậy phương trình có tập nghiệm duy nhất `S={0;1}`

`-> 2` nghiệm

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