Question

Rozwiąż Nierównośći

1.(2x-1)²>16

2.(2-6x)(3x+9)≤x²-9

Answer 1

1.(2x-1)²>16

(2x-1)^2-16>0

(2x-1-4)(2x-1+4)>0

2x-5=0  v   2x+3=0

x=5/2    v   x=3/2

 x e (-,3/2) v (5/2,)

2.(2-6x)(3x+9)≤x²-9

2(1-3x)3(x+3)+9-x^2≤0

2(1-3x)3(x+3)+(3-x)(3+x)≤0

(x+3)(6(1-3x)+3-x)≤0

(x+3)(9-19x)≤0

x+3=0  v   9-19x=0

x=-3    v     x=9/19

x e (-,-3> v <9/19,)