Question

Rozwiąż równania, nierówność:
a) x² - 4x + 4 = 0
b) ( x - 1 )² - 5x ≥ 6x + 5
c) -2x² + 2x 8 > 0
d) 2x² - 2x = 0
c) ( x² - 1 ) ( x² - 4 ) = 0
d) ( x² - 7x +12 ) ( x² - x + 2 ) = 0

Answer 1

1.
Δ=0
x=4/2=2
x={2}
2.
x²-13x-4≥0
√Δ=√185
x1=(13-√185)/2 →
x2=(13+√185)/2 x∈(-∞,13-√185)u (13+√185,∞)
3.
-2x² + 2x +8 > 0
-x² + x +4 > 0
√Δ=√17
x1=(1-√17)/2
x2=(1+√17)/2
x∈((1-√17)/2, (1+√17)/2)
4.
2x² - 2x = 0
x² - x = 0
x(x-1)=0 → x=0 ∨ x=1
x={0,1}
5.
( x² - 1 ) ( x² - 4 ) = 0
x² - 1=0 ∨ x² - 4=0
x=1v x=-1 ∨ x=-2 v x=2
x={-2.-1,1,2}
6.
( x² - 7x +12 ) ( x² - x + 2 ) = 0
x² - 7x +12=0 ∨ x² - x + 2 =0
√Δ=1 Δ<0
x1=3 x∈Ф
x2=4
x={3,4}