If x=3-2√2 find the value of √x + 1/√x I got it to be √8 or 2√2. My method is:- √x + 1/ √x) ^ 2 = x+1/x+2 = x+1/x= 3-2√2 + 1/ 3- 2√2 = 3-2√2 + 3+2√2 =6 = x+1/x = x+1/x+2=(√x+1/√x)^2 =8 Therefore √x+1/√x=√8 This is typed by mistake sorry for this √√xx+1/x√x
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in the step 1, multiply numerator and denominater with the 3+2root2 and simplify
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Answer:
3+2
2
⇒
x
1
=
3+2
2
1
⇒
x
1
=
3+2
2
1
×
(3−2
2
)
(3−2
2
)
=
(3
2
−(2
2
)
2
)
3+2
2
=
9−8
3−2
2
=3−2
2
∴x+
x
1
=3+2
2
+3−2
2
⇒x+
x
1
=6⇒x+
x
1
−2=6−2⇒
⎝
⎛
(
x
)
2
+(
x
1
)
2
−2×
x
×
x
1
⎠
⎞
=4
⇒(
x
−
x
1
)
2
=4⇒
x
−
x
1
=±
4
=±2
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