Odpowiedź:
Wynik obliczeń to 28.
Szczegółowe wyjaśnienie:
[tex][(8-28^{\frac{1}{2}})^{\frac{1}{2}} +(8 + 28^{\frac{1}{2}})^{\frac{1}{2}}]^{2}[/tex]
[tex][(8-\sqrt{28})^{\frac{1}{2}} +(8 + \sqrt{28} )^{\frac{1}{2}}]^{2}[/tex]
Stosujemy wzór: [tex](a+b)^{2} = a^{2} + 2ab + b^{2}[/tex]
[tex]((8-\sqrt{28})^{\frac{1}{2}})^{2} + 2(8-\sqrt{28})^{\frac{1}{2}}(8 + \sqrt{28} )^{\frac{1}{2}} + ((8 + \sqrt{28} )^{\frac{1}{2}})^{2}[/tex]
[tex](8-\sqrt{28}) + 2((8-\sqrt{28})(8 + \sqrt{28}))^{\frac{1}{2}} + (8 + \sqrt{28})[/tex]
Dla środkowego wyrazu stosujemy wzór: [tex](a-b)(a+b) = a^{2} - b^{2}[/tex]
[tex](8-\sqrt{28}) + 2(8^{2} - (\sqrt{28})^{2})^{\frac{1}{2}} + (8 + \sqrt{28})[/tex]
[tex]8-\sqrt{28} + 2(64 - 28)^{\frac{1}{2}} + 8 + \sqrt{28}[/tex]
[tex]16 + 2*36^{\frac{1}{2}}[/tex]
[tex]16 + 2*\sqrt{36}[/tex]
[tex]16 + 2*6[/tex]
[tex]16+12 =28[/tex]
