Question

if =2 + √3 then √x+1/√x =​

Answer 1

Answer:

if=2+√3

Step-by-step explanation:

√x+1/√X

(x+1)/√x

Answer 2

$[tex] \bf\ \underline{ \bigstar \: we \: know \: that \: \: {x}^{2} = \sqrt{x} } \\ \\ \sf\ here \: x = 2 + \sqrt{3} \\ \\ \bf\ \implies: \sqrt{x} = {(2 + \sqrt{3} )}^{2} \\ \\ \bf\ \implies: \sqrt{x} = {2}^{2} + 2 \times 2 \times \sqrt{3} + {( \sqrt{3} )}^{2} \\ \\ \bf\ \implies: \sqrt{x} = 4 + 4 \sqrt{3} + 3 \\ \\\bf\boxed{ \implies: \sqrt{x} = 7 + 4 \sqrt{3}} \\ \\ \sf\ now \: \sqrt{x} + \frac{1}{ \sqrt{x}} = ? \\ \\ \bf\ \implies: (7 + 4 \sqrt{3} )+ ( \frac{1}{7 + 4 \sqrt{3} }) \\ \\ \bf\ \implies: \frac{ {(7 + 4 \sqrt{3} )}^{2} + 1}{7 + 4 \sqrt{3} } \\ \\ \bf\ \implies: \frac{49 + 48 + 56 \sqrt{3} + 1 }{7 + 4 \sqrt{3} } \\ \\ \bf\ \implies: \frac{98 + 56 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ \bf\ \implies: \frac{14( \cancel{7 + 4 \sqrt{3)}} }{ \cancel{7 + 4 \sqrt{3}} } \\ \\\bf\boxed{ \underline{ \implies: 14 }}$[/tex]