Question

if y=√3+1/2 , find y +1/y=?​

Answer 1

$\frac{30 \sqrt{3} }{11} + \frac{7}{11}$

Step-by-step explanation:

$Given, \: \: \: \: y = \sqrt{3} + \frac{1}{2} = \frac{ 2\sqrt{3} + 1}{2} \\ Now, \: \: find\: \: \: y + \frac{1}{y} \\ = \frac{ 2\sqrt{3} + 1}{2} + \frac{1}{\frac{ 2\sqrt{3} + 1}{2}} \\ = \frac{ 2\sqrt{3} + 1}{2} + \frac{2}{2 \sqrt{3} + 1 } \\ = \frac{ 2\sqrt{3} + 1}{2} + \frac{2}{2 \sqrt{3} + 1 } \times \frac{2 \sqrt{3} - 1 }{2 \sqrt{3} - 1} \\ = \frac{ 2\sqrt{3} + 1}{2} + \frac{4 \sqrt{3} - 2}{(2 \sqrt{3} )^{2} - (1) ^{2} } \\ = \frac{ 2\sqrt{3} + 1}{2} + \frac{4 \sqrt{3} - 2}{12 - 1} \\ = \frac{ 2\sqrt{3} + 1}{2} + \frac{4 \sqrt{3} - 2}{11} \\ = \frac{11(2 \sqrt{3} + 1 ) + 2(4 \sqrt{3} - 2)}{22} \\ = \frac{22 \sqrt{3} + 11 + 8 \sqrt{3} - 4 }{11} \\ = \frac{30 \sqrt{3} + 7}{11} \\ = \frac{30 \sqrt{3} }{11} + \frac{7}{11}$