Toán Lớp 8: tìm x biết: (x+7)(5x-6) = (4x+1)(2x-3)

Question

Toán Lớp 8:  tìm x biết: (x+7)(5x-6) = (4x+1)(2x-3)

kimoanh34 · Answer

(x + 7)(5x - 6) = (4x + 1)(2x - 3)   &rArr; x(5x - 6) + 7(5x - 6) = 4x(2x - 3) + (2x - 3)   &hArr; 5x^2 - 6x + 35x - 42 = 8x^2 - 12x + 2x - 3   &hArr; 5x^2 + 29x - 42 = 8x^2 - 10x - 3   &hArr; 8x^2 - 10x - 3 - 5x^2 - 29x + 42 = 0   &hArr; 3x^2 - 39x + 39 = 0   &hArr; 3(x^2 - 13x + 13) = 0   &rArr; x^2 - 13x + 13 = 0   &hArr; x^2 - 2 . x . 13/2 + 169/4 - 169/4 + 52/4 = 0   &hArr; (x - 13/2)^2 - 117/4 = 0   &rArr; (x - 13/2)^2 = 117/4   &rArr; x - 13/2 = &plusmn; sqrt{117}/2   &rArr; x = ( sqrt{117} + 13)/2  v&agrave;  x = (- sqrt{117} + 13)/2    text(Vậy phương tr&igrave;nh c&oacute; nghiệm) S = {( sqrt{117} + 13)/2 ; (- sqrt{117} + 13)/2 }

daithanh · Answer

$(x+7)(5x-6) = (4x+1)(2x-3)$   $ to 5x^2 +29x - 42 = 8x^2 -10x -3$   $ to 3x^2 - 39x + 39 = 0 $   $ to x^2 - 13x +13 = 0 $   $ to 4x^2 - 4.13x + 13.4 = 0 $   $ to (2x)^2 - 2.(2x).13 + 13^2 = 117$   $ to (2x-13)^2 = 117$   $ to  left[  begin{array}{l}x= dfrac{ sqrt[]{117}+13}{2}  x= dfrac{- sqrt[]{117}+13}{2} end{array}  right. $