Question

if x=2√6+7 then find √x+5/√x

Answer 1

x = 2√6 + 7----------( 1 )

1/x = 1/(2√6 + 7) * (2√6 - 7)/(2√6 - 7)

1/x = (2√6 - 7)/(24 - 49)

1/x = (2√6 - 7)/(-25)

25/x = (7 - 2√6)--------( 2 )

adding------( 1 ) & -----( 2 )

x + 25/x = 2√6 + 7 + 7 - 2√6

x + 25/x = 14

(√x)² + (5/√x)² = 14 + 10 - 10

(√x) + (5/√x)² + 2√x * 5/√x = 24

(√x + 5/√x)² = 24

(√x + 5/√x)² = $\bold{+_-2\sqrt{6}}$