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Numbers [#permalink] New post 16 Aug 2007, 03:11
If X+1/X = 4, find the value of X^4 - 1/x^4(x>1)

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X^4 - 1/x^4 = ? Solution [#permalink] New post 16 Aug 2007, 06:57
X^4 - 1/x^4 = ?

we can write it like

(X^2 + 1/x^2)(X^2 - 1/x^2)

1st root (X^2 + 1/x^2)

2nd root (X^2 - 1/x^2)

Soln of 1st root

x + 1/x =4

Now square it

(x + 1/x)^2 =4^2
=>

x^2 + 1/x^2 + 2 = 16
=>
x^2 + 1/x^2 = 14

Soln of 2nd root

(X^2 - 1/x^2)

square it

(X^2 - 1/x^2)^2 =x^4 + 1/x^4 -2 ....... let this is euation 1

Now square the soln of 1st root

(x^2 + 1/x^2)^2 =14^2
=>
x^4 + 1/x^4 + 2 = 196
=>

x^4 + 1/x^4 = 194

Now keep this value into equation 1

(X^2 - 1/x^2)^2 =x^4 + 1/x^4 -2 = 194 - 2 = 192
=> (X^2 - 1/x^2) =sqrt(192) =8 sqrt(3)

Now we got both root

multiple both


(X^2 + 1/x^2)(X^2 - 1/x^2) = 14 * 8 * sqrt(3)
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 [#permalink] New post 16 Aug 2007, 09:17
The Answer is 112 , sqrt (3)
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 [#permalink] New post 16 Aug 2007, 09:24
Eesh. Just figuring out the approach would have taken me at least 1.5 minutes.

Great work, Chiya.
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Thx ! [#permalink] New post 16 Aug 2007, 10:02
Thx everyone !!!

14*8=112...
Thx !   [#permalink] 16 Aug 2007, 10:02
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