Ce trebuie să știm pentru a putea rezolva?:
[tex] \blue{ \bold{Orice \: numar \: la \: puerea \: zero \: da \: 1}}[/tex]
[tex] {x}^{0} = 1 ,\: pentru\: orice \: x\: real[/tex]
[tex] \green{ \bold{Orice \: numar \: la \: puterea \: 1 \: ramne \: neschimbat}}[/tex]
[tex] {x}^{1} = x ,\: pentru \: orice \: x\: real[/tex]
[tex] \orange{ \bold{1 \: la \: orice \: puerea \: da \:1 }}[/tex]
[tex] {1}^{x} = 1 ,\: pentru\: orice \: x \:real[/tex]
1•1•1•...•1=1
Rezolvare:
a)
[tex]( \frac{1}{2} ) {}^{0} + (\frac{1}{2} ) {}^{1} = {}^{2)} 1 + \frac{1}{2} = \\ = \frac{2}{2} + \frac{1}{ 2} = \frac{3}{2} [/tex]
b)
[tex]( \frac{1}{3} ) {}^{0} + (\frac{1}{3} ) {}^{1} = {}^{3)} 1 + \frac{1}{3} = \\ \\ = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} [/tex]
c)
[tex]( \frac{1}{2} ) {}^{1} -( \frac{1}{2}) {}^{2} = \frac{1}{2} - \frac{1 {}^{2} }{2 {}^{2} } = \\ \\ = \frac{1}{2} - \frac{1 \times 1}{2 \times 2} = {}^{2)} \frac{1}{2} - \frac{1}{4} = \\ \\ = \frac{2}{4} - \frac{1}{4} = \frac{1}{4} [/tex]
d)
[tex]( \frac{1}{4} ) {}^{0} - ( \frac{1}{4}) {}^{2} = 1 - \frac{1 {}^{2} }{4 {}^{2} } = 1 - \frac{1 \times 1}{4 \times 4} \\ \\ = {}^{16)} 1 - \frac{1}{16} = \frac{16}{16} - \frac{1}{16} = \frac{15}{16} [/tex]
