Question

Sa se determine solutiile intregi ale inecuatiei:
(x-1)²-9<0

Answer 1

[tex](x-1)^{2}-9\ \textless \ 0 \\ x^{2}-2*x*1+1-9\ \textless \ 0 \\ x^{2}-2*x+-8\ \textless \ 0 \\ d = (-2)^{2} -4*1*(-8) \\ d = 2^{2} +4*8 \\ d = 4 +32 \\ d = 36 \\ x_{1}= \frac{2+6}{2} = \frac{8}{2}=4\\ x_{2}= \frac{2-6}{2} = \frac{-4}{2}=-2\\[/tex]

(Vezi poza)

Ecuatia este mai mica decat 0 daca x∈(-2, 4)
Solutiile intregi ale ecuatiei sunt : (-2, 4) ∩ Z={-1, 0, 1, 2, 3}

Answer 2

x²-2x+1-9<0
x²-2x-8<0
x²-2x-8=0
Δ=4+32
Δ=36
√Δ=6
x₁=(2+6)/2=4
x₂=(2-6)/2=-2
Ecuatia este mai mica decat 0 daca x∈(-2,4)
(-2, 4)∩Z={-1,0,1,2,3}