Question

Tìm x a)(2x+1)(3x-2)+9x²=4 b)x³-4x=0

Answer 1

`# \text {DNamNgV}`

`a)`

`(2x + 1)(3x - 2) + 9x^2 = 4`

`<=> 2x(3x - 2) + 3x - 2 + 9x^2 = 4`

`<=> 6x^2 - 4x + 3x - 2 + 9x^2 = 4`

`<=> 15x^2 - x - 2 = 4`

`<=> 15x^2 - x - 2 - 4 = 0`

`<=> 15x^2 - x - 6 = 0`

`<=> 15x^2 + 9x - 10x - 6 = 0`

`<=> (15x^2 + 9x) - (10x + 6) = 0`

`<=> 3x(5x + 3) - 2(5x + 3) = 0`

`<=> (3x - 2)(5x + 3) = 0`

`<=>` TH1: `3x - 2 = 0`

`<=> 3x = 2`

`<=> x = 2/3`

TH2: `5x + 3 = 0`

`<=> 5x = -3`

`<=> x = -3/5`

Vậy, `x \in {-3/5; 2/3}.`

`b)`

`x^3 - 4x = 0`

`<=> x(x^2 - 4) = 0`

`<=> x*(x^2 - 2^2) = 0`

`<=> x(x - 2)(x + 2) = 0`

`<=>` TH1: `x = 0`

TH2 `x - 2 = 0`

`<=> x = 2`

TH3: `x + 2 = 0`

`<=> x = -2`

Vậy, `x \in {+-2; 0}.`