Question

2+✓3/2-✓3 +2-✓3/2+✓3 + ✓3-1/✓3+1​

Answer 1

Answer:

$\frac{2+\sqrt{3} }{2} -\frac{2-\sqrt{3} }{2+\sqrt{3} } + \frac{\sqrt{3}-1 }{\sqrt{3} +1}\\\= \frac{2+\sqrt{3} }{2} - (\frac{2-\sqrt{3} }{2+\sqrt{3} } )(\frac{2-\sqrt{3} }{2-\sqrt{3} }) +(\frac{\sqrt{3}-1 }{\sqrt{3}+1 })(\frac{\sqrt{3} -1}{\sqrt{3} -1} ) \\= \frac{2+\sqrt{3} }{2} - \frac{(2-\sqrt{3})^2 }{2^2-(\sqrt{3})^2 }+\frac{(\sqrt{3}-1)^2 }{(\sqrt{3}^2-1^2 )}\\= \frac{2+\sqrt{3} }{2} -\frac{4-4\sqrt{3}+3 }{4-3} +\frac{3-6\sqrt{3}+1 }{3-1}$

$= \frac{2+\sqrt{3} }{2} +\frac{4-6\sqrt{3} }{2} -(7-4\sqrt{3} )\\=\frac{2+\sqrt{3}+4-6\sqrt{3}-2(7-4\sqrt{3})}{2} \\=\frac{6-5\sqrt{3} -14 +8\sqrt{3} }{2}\\= \frac{3\sqrt{3} -8}{2}$