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D:
1 - x² > 0
(1 - x)(1 + x) > 0
x ∈(-1, 1)
D = (-1, 1)
log²₂ (1- x²) + log₂(1 - x²) > 0
t = log₂(1 - x²) i x ∈ (-1, 1)
t² + t > 0
t(t +1) > 0
t ∈ (-oo, -1) u (0, +oo)
t < - 1 t > 0
log₂(1 - x²) < - 1 log₂(1 - x²) > 0
log₂(1 - x²) < log₂ 2⁻¹ log₂(1 - x²) > log₂2⁰
1 - x² < 1/2 1 - x² > 1
-x² < - 1/2 -x² > 0
x² > 1/2 x² < 0
x² - 1/2 > 0 x∈{Ф}
(x - √2/2)(x + √2/2) > 0
x ∈ (-oo, -√2/2) u (√2/2, +oo)
x ∈ (-oo, -√2/2) u (√2/2, +oo) lub x ∈ {Ф} ⇒ x ∈ (-oo, -√2/2) u (√2/2, +oo)
x ∈ (-oo, -√2/2) u (√2/2, +oo) i D: x ∈ (-1, 1)
odp. x ∈ (-1 ; -√2/2) u (√2/2, 1)
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D:
1 - x² > 0
(1 - x)(1 + x) > 0
x ∈(-1, 1)
D = (-1, 1)
log²₂ (1- x²) + log₂(1 - x²) > 0
t = log₂(1 - x²) i x ∈ (-1, 1)
t² + t > 0
t(t +1) > 0
t ∈ (-oo, -1) u (0, +oo)
t < - 1 t > 0
log₂(1 - x²) < - 1 log₂(1 - x²) > 0
log₂(1 - x²) < log₂ 2⁻¹ log₂(1 - x²) > log₂2⁰
1 - x² < 1/2 1 - x² > 1
-x² < - 1/2 -x² > 0
x² > 1/2 x² < 0
x² - 1/2 > 0 x∈{Ф}
(x - √2/2)(x + √2/2) > 0
x ∈ (-oo, -√2/2) u (√2/2, +oo)
x ∈ (-oo, -√2/2) u (√2/2, +oo) lub x ∈ {Ф} ⇒ x ∈ (-oo, -√2/2) u (√2/2, +oo)
x ∈ (-oo, -√2/2) u (√2/2, +oo) i D: x ∈ (-1, 1)
odp. x ∈ (-1 ; -√2/2) u (√2/2, 1)