a)
Dziedzina:
[tex]5-x^{2} +4x > 0\\\\-x^{2} +4x+5 > 0\\\\delta=16-4*(-1)*5=36\\\\x_{1}=\frac{-4-6}{-2}=5\\ \\ x_{2}=\frac{-4+6}{-2}=-1\\ \\[/tex]
x∈ (-1 ; 5)
[tex](\frac{1}{2}) ^{-3}=5-x^{2} +4x\\ \\8=5-x^{2} +4x\\\\x^{2} -4x+3=0\\\\delta=16-4*3=4\\\\x_{1}=\frac{4-2}{2}=1\\ \\ x_{2}=\frac{4+2}{2}=3[/tex]
x∈ {1, 3}
b)
[tex]x+1\neq 0\\\\x\neq -1\\\\x+1 > 1\\\\x > 0\\\\x^{2} +3 > 0\\\\x^{2} > -3-zawsze[/tex]
x∈ (1 ; ∞)
[tex](x+1)^{2}=x^{2} +3\\ \\x^{2} +2x+1-x^{2} -3=0\\\\2x-2=0\\\\2x=2\\\\x=1-sprzeczne[/tex]
x∈∅
c)
[tex]4-2x > 0\\\\2x < 4\\\\x < 2[/tex]
x∈ (-∞ ; 2)
[tex]log_{3}(4-2x)\geq 1\\ \\log_{3}(4-2x)\geq log_{3}3\\ \\4-2x\geq 3\\\\-2x\geq -1\\\\x\leq \frac{1}{2}[/tex]
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a)
Dziedzina:
[tex]5-x^{2} +4x > 0\\\\-x^{2} +4x+5 > 0\\\\delta=16-4*(-1)*5=36\\\\x_{1}=\frac{-4-6}{-2}=5\\ \\ x_{2}=\frac{-4+6}{-2}=-1\\ \\[/tex]
x∈ (-1 ; 5)
[tex](\frac{1}{2}) ^{-3}=5-x^{2} +4x\\ \\8=5-x^{2} +4x\\\\x^{2} -4x+3=0\\\\delta=16-4*3=4\\\\x_{1}=\frac{4-2}{2}=1\\ \\ x_{2}=\frac{4+2}{2}=3[/tex]
x∈ {1, 3}
b)
Dziedzina:
[tex]x+1\neq 0\\\\x\neq -1\\\\x+1 > 1\\\\x > 0\\\\x^{2} +3 > 0\\\\x^{2} > -3-zawsze[/tex]
x∈ (1 ; ∞)
[tex](x+1)^{2}=x^{2} +3\\ \\x^{2} +2x+1-x^{2} -3=0\\\\2x-2=0\\\\2x=2\\\\x=1-sprzeczne[/tex]
x∈∅
c)
Dziedzina:
[tex]4-2x > 0\\\\2x < 4\\\\x < 2[/tex]
x∈ (-∞ ; 2)
[tex]log_{3}(4-2x)\geq 1\\ \\log_{3}(4-2x)\geq log_{3}3\\ \\4-2x\geq 3\\\\-2x\geq -1\\\\x\leq \frac{1}{2}[/tex]
x∈ (-∞ ; 2)