Trang chủ » Hỏi đáp » Môn Toán Tìm `x` biết : `(27)^(3x-2)=3^(x^2-1)` 09/08/2024 Tìm `x` biết : `(27)^(3x-2)=3^(x^2-1)`
Trả lời: 27^(3x-2)=3^(x^2-1) <=> (3^3)^(3x-2)=3^(x^2-1) <=> 3^(3(3x-2))=3^(x^2-1) <=> 3^(9x-6)=3^(x^2-1) <=> 9x-6=x^2-1 <=> -x^2+9x-6+1=0 <=> -x^2+9x-5=0 <=> -(x^2-9x+5)=0 <=> -[x^2-2*x*9/2+(9/2)^2-61/4] = 0 <=> -(x-9/2)^2+61/4=0 <=> -(x-9/2)^2=-61/4 <=> (x-9/2)^2=61/4 <=> (x-9/2)^2 = (sqrt(61)/2)^2 TH1: x-9/2=sqrt(61)/2 <=> x = (sqrt(61)+9)/2 TH2: x-9/2=-sqrt(61)/2 <=> x = (-sqrt(61)+9)/2 Vậy S = {(sqrt(61)+9)/2,(-sqrt(61)+9)/2} Trả lời
27^(3x – 2) = 3^(x^2 – 1) (3^3)^(3x – 2) = 3^(x^2 – 1) 3^(9x – 6) = 3^(x^2 – 1) => x^2 – 1 = 9x – 6 x^2 – 1 – 9x + 6 = 0 x^2 – 9x + 5 = 0 x^2 – 9x + 81/4 – 81/4 + 5 = 0 (x – 9/2)^2 – 61/4 = 0 (x – 9/2)^2 = 61/4 x – 9/2 = \pm (sqrt{61})/2 x = ( 9 \pm sqrt{61})/2 Vậy x \in { (9 – sqrt{61})/2 ; ( 9+ sqrt{61})/2} Trả lời
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