Question

if x is equal to 9 + 4 root 5 find the value of root x minus one upon root x

Answer 1

$x = 9 + 4 \sqrt{5} \\ x - \frac{1}{ \sqrt{x} } \\ = 9 + 4 \sqrt{5} - \frac{1}{9 + 4 \sqrt{5} } \\ = (9 + 4 \sqrt{5} ) - \frac{1(9 - 4 \sqrt{5} )}{(9 + 4 \sqrt{5})(9 - 4 \sqrt{5}) } \\ = 9 + 4 \sqrt{5} - \frac{9 - 4 \sqrt{5} }{81 - 80} \\ = 9 + 4 \sqrt{5} - 9 + 4 \sqrt{5} \\ = 8 \sqrt{5}$

Answer 2

Hy

Given
X= 9+4√5

√X= √ 9+4√5
= √ 2sq + (√5)sq +2.2√5

By solving inside bracket we find 9+4√5

= √(2+√5)whole sq
So √x= 2+√5

1/√x= 1/2+√5

= 1/2+√5×2-√5/2-√5

= 2-√5/4-5
= -(2-√5)
= √5 -2

Now √x - 1/√x

= 2+√5 -(√5-2)

= 2+√5-√5+2

= 4 Ans

Hope it helps.....