Question

Rozwiąż nierówności:
a) x²-8x+12<0
b) 2x((x-10)≥4(x-8)
c) -x²+2>0
d) x²-2x-8>0
e) 5(x-1)≤x(3-x)
f) -x²+6<0

Bardzo proszę o pomoc

Answer 1

a) x²-8x+12<0

Δ=64-4*1*12=64-48=16

√Δ=4

x1=(8-4)/2=4/2=2

x2=(8+4)/2=12/2=6

x∈(2,6)

b) 2x((x-10)≥4(x-8)

2x²-20x≥4x-32

2x²-24x+32≥0 //:2

x²-12x+16≥0

Δ=144-4*1*16=144-64=80

√Δ=4√5

x1=(12-4√5)/2=6-2√5

x2(12+4√5)/2=6+2√5

x∈(-∞;6-2√5>u<6+2√5;+∞)

c) -x²+2>0

Δ=-4*(-1)*2=4*2=8

√Δ=2√2

x1=-2√2/-2=√2

x2=2√2/-2=-√2

x∈(-∞;-√2)u(√2;+∞)

d) x²-2x-8>0

Δ=4-4*1*(-8)=4+32=36

√Δ=6

x1=(2-6)/2=-4/2=-2

x2=(2+6)/2=8/2=4

x∈(-∞;-2)u(4;+∞)

e) 5(x-1)≤x(3-x)

5x-5≤3x-x²

5x-5-3x+x²≤0

x²+2x-5≤0

Δ=4-4*1*(-5)=4+20=24

√Δ=2√6

x1=(-2-2√6)/2=-1-√6

x2(-2+2√6)/2=-1+√6

x∈<-1-√6;-1+√6> 

f) -x²+6<0

Δ=-4*(-1)*6=24

√Δ=2√6

x1=-2√6/-2=√6

x2=2√6/-2=-√6

x∈(-∞;-√6)u(√6;+∞)

 

licze na naj