Question

if x = 3+2 root2,, find the value of root x + 1 divided by root x

Answer 1

Step-by-step explanation:

here is your answer.

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Answer 2

Answer:

2 is the value.

Step-by-step explanation:

Given :

$x = 3 + 2\sqrt{2}$

Solution :

$x = 3 + 2 \sqrt2$

$= 1 + 2\sqrt2 + 2$

$=(1 + \sqrt2)2$

$\sqrt x = 1+ \sqrt2$

$\sqrt x + \frac{1}{\sqrt x} = (1 + \sqrt2) + \frac{1}{(1 + \sqrt2)}$

After simplification, we get  

$\sqrt x + \frac{1}{\sqrt x} = 2 \frac{(2 + \sqrt2)}{(1 + \sqrt2)}$

By rationalisation,

$= 2(2+\sqrt{2})(1-\sqrt{2}) /( 1-2)$

$= 2(2-2\sqrt{2}+\sqrt{2} -2 / (-1)$

$=- (2 * (-\sqrt{2} ) )$

$= 2\sqrt{2}$

Hope it helped you.