Question

If x=5-2 root 6 find the value of root x + 1/root x

Answer 1

x=5-2√6
=3+2-2√3√2
=(√3)²-2√3√2+(√2)²
=(√3-√2)²
∴, x=√3-√2
∴, 1/x
=1/√3-√2
=(√3+√2)/(√3-√2)(√3+√2)
=(√3+√2)/{(√3)²-(√2)}
=(√3+√2)/(3-2)
=√3+√2
∴, √x+1/√x
=√3-√2+√3+√2
=2√3

Answer 2

Solution:-
x = 5 - 2√6
1/x = {1/(5 - 2√6)
⇒ 1/x = {1/(5 - 2√6)} × (5 + 2√6)/(5 + 2√6)
= (5 + 2√6)/25 - 24
= 5 + 2√6
Now,
(√x + 1/√x²) = x + 1/x + 2 × √x × 1/√x 
= x + 1/x + 2
⇒ √x + 1/√x = √x + 1/x + 2 (whole root)
= √5 - 2√6 + 5 + 2√6 + 2
= √5 + 5 + 2
= √12
Answer.