Toán Lớp 7: Tìm x: `(3+2x)/(2+3x) = (12)/(13)-5/(13x)`

Question

Toán Lớp 7:  Tìm x: (3+2x)/(2+3x) = (12)/(13)-5/(13x)

tonhitruc · Answer

$  $   (3+2x)/(2+3x) = 12/13 - 5/(13x) (x  ne (-2)/3; x  ne 0)   -> (3+2x)/(2+3x) = (12x)/(13x) - 5/(13x)   ->(3+2x)/(2+3x) = (12x - 5)/(13x)   -> (2 +3x) (12x - 5) = (3+2x).13x   -> 24x - 10 + 36x^2 - 15x = 39x + 26x^2   -> 36x^2 + 9x - 10 - 26x^2 - 39x=0   -> 10x^2 - 30x - 10=0   -> 10 (x^2 - 3x - 1)=0   ->x^2 -3x-1=0   ->x^2 - 2 . x . 3/2 + (3/2)^2 -13/4=0   -> (x-3/2)^2 = 13/4   TH1 :   (x-3/2)^2=( sqrt{13/4})^2   -> x-3/2= sqrt{13/4}   ->x=(3+ sqrt{13})/2 (tm)   TH2 :   (x-3/2)^2=(- sqrt{13/4})^2   ->x-3/2=- sqrt{13/4}   ->x=(3- sqrt{13})/2 (tm)   Vậy x=(3+ sqrt{13})/2 hoặc x=(3- sqrt{13})/2   $  $   Ta chứng minh :   (a+b)^2 = a^2 +2ab + b^2   Vế tr&aacute;i :   =a^2 + ab+ab+b^2   =(a^2+ab)+(ab+b^2)   =a(a+b)+b(a+b)   =(a+b)(a+b)   =(a+b)^2 (Đpcm)