Question

(1+√3) elevado a 2 - (1-√3) elevado a 2 sobre √12

Answer 1

$\displaystyle (1+\sqrt3)^2-\frac{(1-\sqrt3)^2}{\sqrt{12}}\\\\i)~~~~(1+\sqrt3)^2-\frac{(1-\sqrt3)^2}{\sqrt{12}}=1+2\sqrt3+3-\frac{1-2\sqrt3+3}{\sqrt{12}}\\\\ii)~~~\frac{(\sqrt{12}+2\sqrt{36}+3\sqrt{12})-1-2\sqrt3+3}{\sqrt{12}}\\\\iii)~~\frac{4\sqrt{12}+2\sqrt3+10}{\sqrt{12}}=4+2\sqrt{\frac{3}{12}}+\sqrt{\frac{100}{12}}\\\\iv)~~~4+2\sqrt{\frac{3}{12}}+\sqrt{\frac{100}{12}}=4+2(0,5)+2,886751345948128822....\\\\v)~~~~4+2\sqrt{\frac{3}{12}}+\sqrt{\frac{100}{12}}=7,8867513459481288225457439025098\\\\vi)~~~(1+\sqrt3)^2-\frac{(1-\sqrt3)^2}{\sqrt{12}}=4+2\sqrt{\frac{3}{12}}+\sqrt{\frac{100}{12}}\approx\boxed{\boxed{7,9}}$

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