O quadrado do numero: √ [2+√3] +√[ 2-√3 ]
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Olá.
![(\sqrt{2+\sqrt3} + \sqrt{2-\sqrt3})^2\\\\\\
Propriedade \hspace{10} dos\hspace{10} produtos\hspace{10} notaveis:\\
(a+b)^2 = (a^2+2ab+b^2):\\\\\\
(2+\sqrt3)+2(\sqrt{2+\sqrt3})(\sqrt{2-\sqrt3})+(2-\sqrt3)\\\\
2+\sqrt3 + 2 - \sqrt3 + 2[(2+\sqrt3)^\frac{1}{2}.(2-\sqrt3)^\frac{1}{2}]\\\\
Propriedade\hspace{10} dos\hspace{10} produtos\hspace{10} notaveis:\\
(a^x.b^x) = (a.b)^x:\\\\\\
4+ 2[(2+\sqrt3).(2-\sqrt3)}^{\frac{1}{2}}]\\\\\\](https://tex.z-dn.net/?f=%28%5Csqrt%7B2%2B%5Csqrt3%7D+%2B+%5Csqrt%7B2-%5Csqrt3%7D%29%5E2%5C%5C%5C%5C%5C%5C%0APropriedade+%5Chspace%7B10%7D+dos%5Chspace%7B10%7D+produtos%5Chspace%7B10%7D+notaveis%3A%5C%5C%0A%28a%2Bb%29%5E2+%3D+%28a%5E2%2B2ab%2Bb%5E2%29%3A%5C%5C%5C%5C%5C%5C%0A%282%2B%5Csqrt3%29%2B2%28%5Csqrt%7B2%2B%5Csqrt3%7D%29%28%5Csqrt%7B2-%5Csqrt3%7D%29%2B%282-%5Csqrt3%29%5C%5C%5C%5C%0A2%2B%5Csqrt3+%2B+2+-+%5Csqrt3+%2B+2%5B%282%2B%5Csqrt3%29%5E%5Cfrac%7B1%7D%7B2%7D.%282-%5Csqrt3%29%5E%5Cfrac%7B1%7D%7B2%7D%5D%5C%5C%5C%5C%0APropriedade%5Chspace%7B10%7D+dos%5Chspace%7B10%7D+produtos%5Chspace%7B10%7D+notaveis%3A%5C%5C%0A%28a%5Ex.b%5Ex%29+%3D+%28a.b%29%5Ex%3A%5C%5C%5C%5C%5C%5C%0A4%2B+2%5B%282%2B%5Csqrt3%29.%282-%5Csqrt3%29%7D%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%5C%5C%5C%5C%5C%5C "(\sqrt{2+\sqrt3} + \sqrt{2-\sqrt3})^2\\\\\\
Propriedade \hspace{10} dos\hspace{10} produtos\hspace{10} notaveis:\\
(a+b)^2 = (a^2+2ab+b^2):\\\\\\
(2+\sqrt3)+2(\sqrt{2+\sqrt3})(\sqrt{2-\sqrt3})+(2-\sqrt3)\\\\
2+\sqrt3 + 2 - \sqrt3 + 2[(2+\sqrt3)^\frac{1}{2}.(2-\sqrt3)^\frac{1}{2}]\\\\
Propriedade\hspace{10} dos\hspace{10} produtos\hspace{10} notaveis:\\
(a^x.b^x) = (a.b)^x:\\\\\\
4+ 2[(2+\sqrt3).(2-\sqrt3)}^{\frac{1}{2}}]\\\\\\")
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