Question

if x=3-2√2, find the value of√x+1/√x​

Answer 1

Answer:

x=3+22⇒x1=3+221

⇒x1=3+221×(3−22)(3−22)=(32−(22)2)3+22=9−83−22=3−22

∴x+x1=3+22+3−22

⇒x+x1=6

Answer 2

$x = 3 - 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \\ \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \frac{1}{x} = 3 + 2 \sqrt{2} \\ \\ x + \frac{1}{x} = 6 \\ x + \frac{1}{x} + 2 = 8 \\ ( { \sqrt{x} + \frac{1}{ \sqrt{x} } })^{2} = 8 \\ \sqrt{x} + \frac{1}{ \sqrt{x} } = 2 \sqrt{2}$