Question

Rozwiąż nierówność:

1. (x-2)(x+2)<9

2.(3-x)(3+x)>3(x-2)^2

3.√2x^2-2x+1<0

Answer 1

1. (x-2)(x+2)<9

x^2 + 2x - 2x - 4 < 9

x^2 - 4 < 9

x^2 < 13

x < √13

 

2.(3-x)(3+x)>3(x-2)^2

9 + 3x - 3x - x^2 > 3(x^2 - 4x + 4)

9 - x^2 > 3x^2 - 12x + 12

-x^2 - 3x^2 - 12x > 12 - 9

-4x^2 - 12x > 3

-4x^2 - 12x - 3 > 0

 

delta = b^2 - 4ac

delta = 144 - 48

delta = 96

 

x1 = (-b-√delta)/2a

x1 = (12 - √16*6) / (-8)

x1 = (12 - 4√6)/(-8)

x1 = -96 + 32√6

 

x2 = (-b+√delta)/2a

x2 = (12 + √16*6) / (-8)

x2 = (12 + 4√6)/(-8)

x2 = -96 - 32√6

 

3.√2 * x^2-2x+1<0

delta = b^2 - 4ac

delta = 4 - 4 * √2 * 1

delta = 4 - 4√2

 

x1 = (-b - √delta)/2a

x2 = (-b + √delta)/2a