if x = 3+2√2 then the value of (√x-1/√x=
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1
Answer:
Let √x - 1/√x = a
Squaring both the sides,
x + 1/x - 2 = a^2
Putting the value,
3–2√2 + 1/(3–2√2) - 2 = a^2
a^2 = 1 - 2√2 + 1/(3–2√2)
= [(3–2√2) (1–2√2) + 1] / 3–2√2
= {3 - 8√2 + 9} / 3–2√2
= [12 - 8√2] / 3–2√2
Rationalising both the sides
= {(12 - 8√2)(3+2√2)} ÷ (9–8)
= 36 + 24√2 - 24√2 + 16(2)
= 36 - 32
=> 4
a^2 = 4
a = √4
a = 2, -2
So,
√x - 1/√x = a = 2, -2
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Answered by
19
Answer:
x=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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