Question

联立方程(三题)

Answer 1

1. {y=x^2-2x+3 y=3x-1 3x - 1 = x^2 - 2x + 3 x^2 - 2x - 3x + 1 + 3 = 0 x^2 - 5x + 4 = 0 (x - 1)(x - 4) = 0 x - 1 = 0
x - 4 = 0 x = 1
x = 4 2. {y=4x^2-3x+2 y=8x+5 8x + 5 = 4x^2 - 3x + 2 4x^2 - 3x - 8x - 5 + 2 = 0 4x^2 - 11x - 3 = 0 (4x + 1)(x - 3) = 0 4x + 1 = 0
x - 3 = 0 x = -0.25
x = 3 3. {y=-3x xy-3=6x x(-3x) - 3 = 6x -3x^2 - 3 = 6x -3x^2 - 6x - 3 = 0 3x^2 + 6x + 3 = 0 (3x + 3)(x + 1) = 0 3x + 3 = 0
x + 1 = 0 x = -1
x = -1
参考: me
(Question 1) y=x^2-2x+3 -----(i) y=3x-1 ----(ii) Sub(ii) into (i) :3x-1 = x^2-2x+3 x^2-5x+4=0 (x-4)(x-1)=0 Therefore
x=4 or x=1 y=3(4)-1 or y=3(1)-1 =11 or y=2 Solutions are(4
11) and (1
2) (Question 2) y=4x^2-3x+2 y=8x+5 8x+5 = 4x^2-3x+2 4x^2-11x-3 (4x+1)(x-3) = 0 Therefore x =-1/4 or x=3 y=8(-1/4)+5 or y=8(3)+5 =3 or y=29 Solutions are(-1/4
3) and (3
29) (Question 3) y=-3x xy-3=6x x(-3x)-3=6x -3x^2-6x-3=0 x^2+2x+1=0 (x+1)^2=0 x=-1 y=-3(-1) =3 The solution is(-1
3)
1. {y=x²-2x+3 .......... (1) y=3x-1 ............ (2) 从(1) = (2)， x²-2x+3 = 3x-1 x²-5x+4 = 0 (x-4)(x-1) = 0 x-4 = 0 或 x-1 = 0 x=4 或 x=1 若 x=4
y = 3(4)-1 = 11 ....... 从 (2) 若 y = 1 y = 3(1)-1 = 2 ........ 从 (2) 所以 x=4
y=11 或 x=1
y=2 =================================== 2. {y=4x²-3x+2 .......... (1) y=8x+5 ............ (2) 从(1) = (2)， 4x²-3x+2 = 8x+5 4x²-11x-3 = 0 (4x+1)(x-3) = 0 4x+1 = 0 或 x-3 = 0 x = -1/4 或 x = 3 若 x=-1/4
y = 8(-1/4)+5 = 3 ........ 从 (2) 若 x=3
y = 8(3)+5 = 29 ........ 从 (2) 所以 x=-1/4
y=3 或 x=3
y=29 =================================== 3. {y=-3x .......... (1) xy-3=6x ............ (2) 将 (1) 代入 (2) x(-3x)-3 = 6x -3x² - 3 = 6x 3x² + 6x + 3 = 0 x² + 2x + 1 = 0 (x+1)² = 0 x+1 = 0 x = -1 若 x = -1
y = -3(-1) = 3 所以 x=-1
y=3