Question

(2x-3)(x+4)<2(x-2)²+2

Answer 1

(2x - 3)(x + 4) < 2(x - 2)² + 2

<=> 2x² + 5x - 12 - 2(x² - 4x + 4) - 2 < 0

<=> 2x² + 5x -14 - 2x² + 8x - 8 < 0

<=> 13x - 22 < 0

<=> 13x < 22

<=> x < 22/13

Answer 2

`(2x-3)(x+4)<2(x-2)^2 +2`

`<=>2x^2 -3x +8x -12<2(x^2 -4x+4)+2`

`<=>2x^2 +5x -12<2x^2 -8x+8+2`

`<=>2x^2 +5x -12<2x^2 -8x+10`

`<=>2x^2 +5x -12-2x^2 +8x-10 <0`

`<=>13x-22<0`

`<=>13x<22`

`<=>x < 22/13`

Vậy bất phương trình có nghiệm `x< 22/13`