Question

SOLVE:-
[tex]






\sqrt{30- \sqrt{30- \sqrt{30-} } } .................. \infty}

[/tex]

AND 

$If x= 2+ \sqrt{3} find \sqrt{x} - \frac{1}{ \sqrt{x} }$

Answer 1

let 
y = √{30-√(30)-√(30- ................∞)}
y = √(30-y)
y² = 30-y
y² + y - 30 = 0
y² + 6y - 5y - 30 = 0
y(y+6) -5(y+6) = 0
(y+6)(y-5) = 0
y = 5 , -6


(ii)  x = 2+√3
√x - 1/√x
= (x-1)/√x
= (2+√3 - 1)/(2+√3)
= (1+√3)(2-√3)/{(2+√3)(2-√3)
= (2+2√3 - √3 - 3)/(4-3)
= √3 - 1