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1.
2 x 2 − 11 x + 21 = 3 4 x − 4 3 2x^2-11x+21=3\sqrt[3]{4x-4} 2 x 2 − 1 1 x + 2 1 = 3 3 4 x − 4 V T = 2 ( x − 11 4 ) 2 + 47 8 > 0 ⇒ 4 x − 4 3 > 0 1 8 ( 4 x − 4 ) 2 − 7 4 ( 4 x − 4 ) − 3 4 x − 4 3 + 12 = 0 t = 4 x − 4 3 > 0 t 6 − 14 t 3 − 24 t + 96 = 0 ⇒ ( t − 2 ) 2 ( t 4 + 4 t 3 + 12 t 2 + 18 t + 24 ) = 0 t = 2 ⇒ x = 3 t 4 + 4 t 3 + 12 t 2 + 18 t + 24 > 0 ⇒ v o ^ − n g h i ệ m VT = 2(x-\frac{11}{4})^2 + \frac{47}{8} > 0 \Rightarrow \sqrt[3]{4x-4} > 0 \\ \\ \frac{1}{8}(4x-4)^2 - \frac{7}{4}(4x-4) - 3\sqrt[3]{4x-4}+12 = 0 \\ \\ t = \sqrt[3]{4x-4} > 0 \\ \\ t^6 -14t^3-24t+96 = 0 \Rightarrow (t-2)^2(t^4+4t^3+12t^2+18t+24) = 0 \\ \\ t = 2 \Rightarrow x =3 \\ \\ t^4+4t^3+12t^2+18t+24 > 0 \Rightarrow vô-nghiệm V T = 2 ( x − 4 1 1 ) 2 + 8 4 7 > 0 ⇒ 3 4 x − 4 > 0 8 1 ( 4 x − 4 ) 2 − 4 7 ( 4 x − 4 ) − 3 3 4 x − 4 + 1 2 = 0 t = 3 4 x − 4 > 0 t 6 − 1 4 t 3 − 2 4 t + 9 6 = 0 ⇒ ( t − 2 ) 2 ( t 4 + 4 t 3 + 1 2 t 2 + 1 8 t + 2 4 ) = 0 t = 2 ⇒ x = 3 t 4 + 4 t 3 + 1 2 t 2 + 1 8 t + 2 4 > 0 ⇒ v o ^ − n g h i ệ m
1. Ta thấy : 2 x 2 − 11 x + 21 = 2 ( x − 11 4 ) 2 + 47 8 > 0 2x^{2}-11x+21 = 2( x- \frac{11}{4})^{2}+ \frac{47}{8} > 0 2 x 2 − 1 1 x + 2 1 = 2 ( x − 4 1 1 ) 2 + 8 4 7 > 0 3 4 x − 4 3 > 0 ⟺ x − 1 > 0 3\sqrt[3]{4x-4}> 0\iff x-1 > 0 3 3 4 x − 4 > 0 ⟺ x − 1 > 0 C a u c h y Cauchy C a u c h y 2 ( x − 1 ) 2 + 8 ≥ 8 ( x − 1 ) 2(x-1)^{2}+ 8 \geq 8(x-1) 2 ( x − 1 ) 2 + 8 ≥ 8 ( x − 1 ) ( x − 1 ) + 2 + 2 ≥ 3 4 ( x − 1 ) 3 (x-1) +2+ 2 \geq 3\sqrt[3]{4(x-1)} ( x − 1 ) + 2 + 2 ≥ 3 3 4 ( x − 1 ) 2 ( x − 1 ) 2 − 7 ( x − 1 ) + 12 ≥ 3 4 ( x − 1 ) 3 2 (x-1)^{2} - 7(x-1)+12\geq 3\sqrt[3]{4(x-1)} 2 ( x − 1 ) 2 − 7 ( x − 1 ) + 1 2 ≥ 3 3 4 ( x − 1 ) ⟺ 2 x 2 − 11 x + 21 ≥ 3 4 ( x − 1 ) 3 \iff 2x^{2}-11x +21\geq 3\sqrt[3]{4(x-1)} ⟺ 2 x 2 − 1 1 x + 2 1 ≥ 3 3 4 ( x − 1 ) x − 1 = 2 ⟺ x = 3 x-1= 2 \iff x=3 x − 1 = 2 ⟺ x = 3
2. p t ⟺ x 2 − 22 x + 40 + 21 ( x 4 + x 2 + 1 ) − 21 = 0 ⟺ ( x − 2 ) ( x − 20 ) + 21 ( x − 2 ) ( x + 2 ) ( x 2 + 5 ) 21 ( x 4 + x 2 + 1 ) + 21 = 0 2. \ \ pt\iff x^2-22x+40+\sqrt{21(x^4+x^2+1)}-21=0 \\ \iff (x-2)(x-20)+\dfrac{21(x-2)(x+2)(x^2+5)}{\sqrt{21(x^4+x^2+1)}+21}=0 2 . p t ⟺ x 2 − 2 2 x + 4 0 + 2 1 ( x 4 + x 2 + 1 ) − 2 1 = 0 ⟺ ( x − 2 ) ( x − 2 0 ) + 2 1 ( x 4 + x 2 + 1 ) + 2 1 2 1 ( x − 2 ) ( x + 2 ) ( x 2 + 5 ) = 0
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn