Trang chủ » Hỏi đáp » Môn Toán tìm x : ( 2x – 1 ) mũ 4 = ( 2x – 1 ) mũ 6 19/12/2024 tìm x : ( 2x – 1 ) mũ 4 = ( 2x – 1 ) mũ 6
(2x – 1)^4 = (2x – 1)^6 => (2x – 1)^6 – (2x – 1)^4 = 0 => [(2x – 1)^4] . [(2x – 1)^2 – 1] = 0 => (2x – 1)^4 = 0 hoặc (2x – 1)^2 – 1 = 0 TH1) (2x – 1)^4 = 0 => 2x – 1 = 0 => 2x = 1 => x = 1/2 TH2) (2x – 1)^2 – 1 = 0 => (2x – 1)^2 = 1 => 2x – 1 = ± 1 TH1: 2x – 1 = 1 => 2x = 2 => x = 1 TH2: 2x – 1 = -1 => 2x = 0 => x = 0 Vậy x = 1/2 ; 1; 0 Trả lời
Giải đáp: x \in {1/2;1;0} Lời giải và giải thích chi tiết: (2x-1)^4 = (2x-1)^6<=>(2x-1)^4 – (2x-1)^6 = 0<=>(2x-1)^4 – (2x-1)^4 . (2x-1)^2 = 0<=>(2x-1)^4 .[1 – (2x-1)^2] = 0<=>\(\left[ \begin{array}{l}(2x-1)^4 = 0\\1 – (2x-1)^2 = 0\end{array} \right.\) <=>\(\left[ \begin{array}{l}2x-1=0\\2x-1 = 1\end{array} \right.\) <=>\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=1\\x=0\end{array} \right.\) Vậy x \in {1/2;1;0} Trả lời
<=>(2x-1)^4 – (2x-1)^6 = 0
<=>(2x-1)^4 – (2x-1)^4 . (2x-1)^2 = 0
<=>(2x-1)^4 .[1 – (2x-1)^2] = 0
<=>\(\left[ \begin{array}{l}(2x-1)^4 = 0\\1 – (2x-1)^2 = 0\end{array} \right.\) <=>\(\left[ \begin{array}{l}2x-1=0\\2x-1 = 1\end{array} \right.\) <=>\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=1\\x=0\end{array} \right.\)
Vậy x \in {1/2;1;0}