Toán Lớp 8: Tìm x A) (x-2)²-(x-1)²=9 B) (x-1)²+x(1-x)=0 C) (x+4)²-(x+3)²=7 D) (2x-1)²-2(2x+1)(x-4)=35

Question

Toán Lớp 8:  Tìm x A)  (x-2)²-(x-1)²=9 B)  (x-1)²+x(1-x)=0 C)  (x+4)²-(x+3)²=7 D)  (2x-1)²-2(2x+1)(x-4)=35

quynhmaithu · Answer

Giải đáp:   a)x=-3   b)x=1   c)x=0   d)x=13/5   Lời giải và giải thích chi tiết:   a)(x-2)&sup2;-(x-1)&sup2;=9   &hArr;x&sup2;-4x+4-(x&sup2;-2x+1)=9   &hArr;x&sup2;-4x+4-x&sup2;+2x-1=9   &hArr;(x&sup2;-x&sup2;)+(-4x+2x)+(4-1)=9   &hArr;-2x+3=9   &hArr;-2x=9-3   &hArr;-2x=6   &hArr;x=6:(-2)   &hArr;x=-3   Vậy x=-3   b)(x-1)&sup2;+x(1-x)=0   &hArr;(x-1)&sup2;-x(x-1)=0   &hArr;(x-1-x)(x-1)=0   &hArr;-(x-1)=0   &hArr;-x+1=0   &hArr;-x=-1   &hArr;x=1   Vậy x=1   c)(x+4)&sup2;-(x+3)&sup2;=7   &hArr;x&sup2;+8x+16-(x&sup2;+6x+9)=7   &hArr;x&sup2;+8x+16-x&sup2;-6x-9=7   &hArr;(x&sup2;-x&sup2;)+(8x-6x)+(16-9)=7   &hArr;2x+7=7   &hArr;2x=7-7   &hArr;2x=0   &hArr;x=0   Vậy x=0   d)(2x-1)&sup2;-2(2x+1)(x-4)=35   &hArr;4x&sup2;-4x+1+(-4x-2)(x-4)=35   &hArr;4x&sup2;-4x+1-4x&sup2;+16x-2x+8=35   &hArr;(4x&sup2;-4x&sup2;)+(-4x+16x-2x)+(1+8)=35   &hArr;10x+9=35   &hArr;10x=35-9   &hArr;10x=26   &hArr;x=26/10   &hArr;x=13/5   Vậy x=13/5

thanoanghha · Answer

Giải đáp:       Lời giải và giải thích chi tiết:   a)   (x-2)^2 - (x-1)^2 = 9   -> x^2 - 4x + 4 - x^2 + 2x - 1 = 9   -> (x^2-x^2) + (-4x+2x) + (4-1) = 9   -> -2x + 3 = 9   -> -2x = 6   -> x = -3   Vậy x  in {-3}   b)   (x-1)^2 + x(1-x) = 0   -> x^2 - 2x + 1 + x - x^2 = 0   -> (x^2-x^2) -2x + x + 1 = 0   -> -x + 1 = 0   -> -x = -1   -> x = 1   Vậy x in{1}   c)   (x+4)^2 - (x+3)^2 = 7   -> x^2 + 18x + 16 - x^2 - 6x - 9 = 7   -> (x^2-x^2) + (8x-6x) + (16-9) = 7   -> 2x + 7 = 7   -> 2x = 0   -> x = 0   Vậy x  in {0}   d)   (2x-1)^2 - 2(2x+1)(x-4)=35   -> 4x^2 - 4x + 1 - 4x^2 + 14x + 8 = 35   -> (4x^2-4x^2) + (-4x+14x) + (1+8) = 35   -> 10x + 9 =35   -> 10x = 26   -> x = 13/5   Vậy x  in {13/5}