Question

do rozwiazania nierownosci kwadratowe

a)−3(x−2)(x+4)>0

b)1/2(x+1)(x−1)≥0

c)−5(x−√2)(x+3√2)≥0

d)2(x−7)x<0

e)−x(2x−5)≤0

f)3(x+6)2≤0

Answer 1

a)−3(x−2)(x+4)>0----- / : (-3)

(x - 2)(x  +4) < 0

x ∈ (-4, 2)

 

b)1/2(x+1)(x−1)≥0 --- / : 1/2

(x + 1)(x - 1) ≥ 0

x ∈ (-oo, -1) u (1, +oo)

 

c)−5(x−√2)(x+3√2)≥0

(x−√2)(x+3√2) ≤ 0

x ∈ (-3√2, √2)

 

d)2(x−7)x<0

x(x - 7) < 0

x ∈ (0, 7)

 

e)−x(2x−5)≤0

x(2x - 5) ≥ 0

x ∈ (-oo, 0) u (2,5, + oo)

 

f)3(x+6)²≤0

(x+6)²≤0

x ∈ R

 

Answer 2

a) -3(x-2)(x+4)>0  /:(-3)

(x-2)(x+4)<0

x 1=2    x 2=-4

x nalezy (-4;2)

b)    1/2(x+1)(x-1)≥0   /·2

(x+1)(x-1)≥0

x 1=-1      x 2=1

xE(-∞;-1>U<1;∞0

 

c)-5(x-√2)(x+3√2)≥0     /(-5)

(x-√2)(x+3√2)≤0

x 1=√2          x 2=-3√2

xE(-∞;-3√2>U<√2:∞)

 

d)   2(x-7)x<0   /:2

x(x-7)<0

x 1=0        x 2=7

xE(0;7)

 

e)-x(2x-5)≤0   /·(-1)

x(2x-5)≥0

x 1=0       x 2=5/2

xE(-∞;0>U<5/2;∞)

 

f)  3(x+6)2≤0     /:6

x+6≤0

x≤-6

xE(-∞;-6>