1) a) (x-3)²-9=0
<=> (x-3)²=9
<=> x-3=±√9
<=> x-3=±3
<=> x=0 hoặc x=6
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b) (2x-5)² - x² -4x -4=0
<=> 4x² - 20x +25 - x² -4x -4=0
<=> 3x² -24x +21 =0
<=> 3x² -3x -21x +21=0
<=> 3x(x-1) -21 (x-1) =0
<=> (x-1)(3x-21)=0
<=> \(\left[ \begin{array}{l}x-1=0\\3x-21=0\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x=0\\x=7\end{array} \right.\)
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c) $x^4$ +6x² +8=0
<=> $x^4$ +4x²+2x² +8=0
<=> x²(x²+4) + 2(x²+4)=0
<=> (x²+4)(x²+2)=0
<=> \(\left[ \begin{array}{l}x²+4=0\\x²+2=0\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x^2=-4(vô lý)\\x^2=-2(vô lý)\end{array} \right.\)
Vậy PT vô nghiệm
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2) đặt $x^2$+2x+2=a
PT <=>a(a+1)-2=0
<=> a²+a-2=0
<=> a² +2a-a-2=0
<=> a(a+2)-(a+2)=0
<=> (a+2)(a-1)=0
<=> a=-2 hoặc a=1
+) Với a=-2
=> $x^2$+2x+2=-2
<=> $x^2$+2x+4=0
PT vô nghiệm
+) với a=1
<=> $x^2$+2x+2=1
<=> $x^2$+2x+1=0
<=> (x+1)²=0
=> x+1=0
x=-1
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