Question

If x = 4 + 2√3 find the value of √x + 1/√x

Answer 1

Answer:

${( \sqrt{x} + \frac{1}{ \sqrt{x} }) }^{2} = x + \frac{1}{x} + 2 \\ \\ = 4 + 2 \sqrt{3} + \frac{1}{4 + 2 \sqrt{3} } + 2 \\ = \frac{16 + 12 + 16 \sqrt{3} + 1}{4 + 2 \sqrt{3} } + 2 \\ \\ = \frac{29 + 16 \sqrt{3} }{4 + 2 \sqrt{3} } + 2 = \frac{37 + 20 \sqrt{3} }{4 + 2 \sqrt{3} } \\ \\ \sqrt{x } + \frac{1}{ \sqrt{x} } = \sqrt{ \frac{37 + 20 \sqrt{3} }{4 + 2 \sqrt{3} } }$