Question

Giải phương trình: (x²+x+1)²=3(x⁴+x²+1)

Answer 1

 

(x²+x+1)²=3(x⁴+x²+1)

<=>x⁴+x²+1+2x³+2x²+2x=3x⁴+3x²+3

<=>x⁴+2x³+3x²+2x+1=3x⁴+3x²+3

<=>2x⁴-2x³-2x+2=0

<=>2x³.(x-1)-2.(x-1)=0

<=>2.(x-1)(x³-1)=0

<=>2.(x-1)(x-1)(x²+x+1)=0

<=>2.(x-1)².(x²+x+1)=0

<=>x-1=0 ( vì x²+x+1=(x+1/2)²+3/4 >0))

<=>x=1

Answer 2

<=> x⁴+x²+1+2x³+2x²+2x=3x⁴+3x²3
<=> 2x³+2x=2x⁴+2
<=> -2x⁴+2x³+2x-2=0
<=> -2x³(x-1) +2(x-1)=0
<=> (-2)(x-1)(x³-1)=0
<=> (-2)(x-1)²(x²+2x+1)
<=> (-2)(x-1)²((x+1/2)²+3/4)
<=> x-1=0
<=> x=0