Odpowiedź:
a) [tex]x^{0}[/tex] = (2x + 3)
2x + 3 = 1
2x = -2
x = -1
b) [tex]x^{3}[/tex] = [tex]\frac{1}{8}[/tex]
x = [tex]\sqrt[3]{\frac{1}{8}}[/tex]
x = [tex]\frac{1}{2}[/tex]
c) [tex]x^{-3}[/tex] = [tex]\frac{1}{27}[/tex]
[tex](\frac{1}{x}) ^{3}[/tex] = [tex]\frac{1}{27}[/tex]
[tex]\frac{1}{x^{3}}[/tex] = [tex]\frac{1}{27}[/tex]
[tex]x^{3}[/tex] = 27
x = 3
d) [tex](2x - 5)^{2}[/tex] = 16
4[tex]x^{2}[/tex] - 20x + 25 = 16
4[tex]x^{2}[/tex] - 20x + 9 = 0
Δ = 400 - 4(4)(9) = 400 - 144 = 256
[tex]\sqrt{delta}[/tex] = 16
x1 = (20 - 16)/8 = 4/8 = [tex]\frac{1}{2}[/tex]
x2 = (20 + 16)/8 = 36/8 = 4,5
e) [tex]\sqrt{3-x}^{-2}[/tex] = [tex]\frac{1}{4}[/tex]
[tex](\frac{1}{\sqrt{3-x}}) ^{2}[/tex] = [tex]\frac{1}{4}[/tex]
3 - x = 4
-x = 1
x = -1
f) [tex](x^{2})^{3}[/tex] = 27
[tex]x^{2}[/tex] = [tex]\sqrt[3]{27}[/tex]
[tex]x^{2}[/tex] = 3
x = [tex]\sqrt{3}[/tex]
