Question

if x=7-4 V3 find the value of √x+1/√x​

Answer 1

$x = 7 - 4 \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{7 - 4 \sqrt{3} } \\ \frac{1}{x} = \frac{1}{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \frac{1}{x} = \frac{7 + 4 \sqrt{3} }{49 - 48} \\ \frac{1}{x} = 7 + 4 \sqrt{3} \\ \\ x + \frac{1}{x} = 14 \\ x + \frac{1}{x} + 2 = 16 \\ ( { \sqrt{x} + \frac{1}{ \sqrt{x} } })^{2} = 16 \\ \sqrt{x} + \frac{1}{ \sqrt{x} } =± 4$