if x = 3+2 root 2 find find root x+1/root x - Maths -

Question

if x = 3+2 root 2 find find root x+1/root x

Sanidhya · Accepted Answer

x = 3 +
2√2
=> √x = √(3+
2√2)
=>
√[{(√2)2+
(√1)2 +
(2)(√2)(√1)}]
=> √(√2+
√1)2 [a2+b2+2ab =
(a+b)2]
=> √2+
√1
Putting the value of √x in the given
expression, (√2+
√1)+1/(√2+ √1)
=> (√2+ 1+1)/(
√2+ 1 )
=> (√2+ 2)/
√2+ 1
rationalising the
expression we get, {(√2+
2) (√2
-1)}/(√2+
1)(√2- 1
)
=> √2