Maths 二次方程

1. (3x+2)(3x+1)=20
(3x)(3x) + (3x)(1) + (2)(3x) + (2)(1) = 20
9x^2 + 3x + 6x + 2 - 20 = 0
9x^2 + 9x - 18 = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0
For (x + 2) = 0, x = -2
For (x - 1) = 0, x = 1

Ans. x = 1 or x = -2

2. 3x(4x-1)=(2x+1)^2
12x^2 - 3x = 4x^2 + 4x + 1
12x^2 - 3x - 4x^2 - 4x - 1 = 0
8x^2 - 7x - 1 = 0
(8x +1)(x - 1) = 0
For (8x + 1) = 0, x = - (1/8)
For (x - 1) = 0, x = 1

Ans. x = 1 or x = - (1/8)

3. (x+2)(3x-2)=(x+6)(2x+1)
(x)(3x) + (x)(-2) + (2)(3x) + (2)(-2) = (x)(2x) + (x)(1) + (6)(2x) + (6)(1)
3x^2 - 2x + 6x - 4 = 2x^2 + x +12x + 6
3x^2 - 2x + 6x - 4 - 2x^2 - x - 12x - 6 = 0
x^2 - 9x - 10 = 0
(x + 1)(x - 10) = 0
For (x + 1) = 0, x = -1
For (x - 10) = 0, x = 10

Ans. x = 10 or x = -1

4. (x-3)^2=(1-4x)^2
x^2 - 6x + 9 = 1 - 8x + 16x^2
x^2 - 6x + 9 - 1 + 8x - 16x^2 = 0
-15x^2 - 2x + 8 = 0
(Multiply all by -1),
15x^2 + 2x - 8 = 0
(3x - 2)(5x + 4) = 0
For (3x - 2) = 0, x = 2/3
For (5x + 4) = 0, x = - (4/5)

Ans. x = 2/3 or x = - (4/5)


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