[Toán 9] Giải các PT sau

L

lp_qt

1. $$x^3+x^2-3x+9=0 \iff (x+3)(x^2-2x+3)=0 \iff x=-3$$

2. $$x^4-4x=1 \iff x^4+2x^2+1=2(x^2+2x+1) \iff (x^2+1)^2=2.(x+1)^2 \iff \begin{bmatrix} x^2+1=\sqrt{2}(x+1) & \\ x^2+1=-\sqrt{2}(x+1) & \end{bmatrix} \iff ...$$
 
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Q

quynhphamdq

[TEX]1. x^3+x^2-3x+9=0[/TEX]
[TEX]\Rightarrow x^3 +3x^2 - 2x^2 - 6x + 3x +9 =0 [/TEX]
[TEX]\Rightarrow x^2 (x+3)- 2x(x+3) +3(x+3) = 0[/TEX]
\Rightarrow [TEX](x^2 -2x+3) (x+3)=0[/TEX]
Vì [TEX]x^2 -2x +3 = x^2 -2x +1 +2 = (x-1)^2 +2 \geq 2[/TEX]
[TEX]\Rightarrow x+3 =0 \Rightarrow x= -3.[/TEX]
 
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