Question

rozwiąż nierówności :

a) (X+4)²-(X+1)² ≥ 4(x-1)

b) (x-2)²-(X+5)(x-5)>-4(X+5)

c) 4 (x-1)(X+1)-(2x-1)²>3

Answer 1

a) (x+4)²-(x+1)² ≥ 4(x-1)

x²+8x+16-(x²+2x+1)≥4x-4

x²+8x+16-x²-2x-1≥4x-4

2x≥-19 /:2

x≥-19/2

x≥-9i1/2

 

b) (x-2)²-(x+5)(x-5)>-4(x+5)

x²-4x+4-(x²-25)>-4x-20

x²-4x+4-x²+25>-4x-20

0x>-49

x>0

 

c) 4 (x-1)(x+1)-(2x-1)²>3

4(x²-1)-(4x²-4x+1)>3

4x²-4-4x²+4x-1>3

4x>8   /:4

x>2

Answer 2

a)

(x+4)²-(x+1)² ≥ 4(x-1)

x²+2*4*x+4²-(x²+2*x*1+1²)≥ 4x-4

x²+8x+16-(x²+2x+1)≥ 4x-4

x²+8x+16-x²-2x-1≥ 4x-4

8x-2x-4x≥-4+1-16

2x≥-19 /:2

x≥-9,5

 

b)

(x-2)²-(x+5)(x-5)> -4(x+5)

(x²-2*x*2+2²)-(x²-5x+5x-25)> -4x-20

(x²-2*x*2+2²)-(x²-25)> -4x-20

(x²-4x+4)-x²+25> -4x-20

x²-4x+4-x²+25> -4x-20

-4x+4x>-20-4-25

0x>-49

x>0

 

 

c)

4(x-1)(x+1)-(2x-1)²>3

4(x²+x-x-1)-[(2x)²-2*2x*1+1²]>3

4(x²+x-x-1)-(4x²-4x+1)>3

4(x²-1)-4x²+4x-1>3

4x²-4-4x²+4x-1>3

4x>3+1+4

4x>8 /:4

x>2