x^2 +1/x^2=7 , x is greater than 0 find the value of x3+1/x3 and x-1/x
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Answered by
3
Given x^2 + 1/x^2 = 7
We know (x + 1/x)^2 = x^2 + 1/x^2 + 2
= 7 + 2
= 9.
(x + 1/x) = 3.
On cubing both sides, we get
(x + 1/x)^3 = 3^3.
x^3 + 1/x^3 + 3(x + 1/x) = 27
x^3 + 1/x^3 + 3(3) = 27
x^3 + 1/x^3 + 9 = 27
x^3 + 1/x^3 = 27 - 9
x^3 + 1/x^3 = 18. ------------------- (1)
Given x^2 + 1/x^2 = 7
We know that (x - 1/x)^2 = x^2 + 1/x^2 - 2 * 1/x
= x^2 + 1/x^2 - 2
= 7 - 2
= 5.
Then (x - 1/x) = root 5. --------------- (2)
.
From (1) & (2),
The value of x^3 + 1/x^3 = 18.
The value of x - 1/x = root 5.
Hope this helps!
We know (x + 1/x)^2 = x^2 + 1/x^2 + 2
= 7 + 2
= 9.
(x + 1/x) = 3.
On cubing both sides, we get
(x + 1/x)^3 = 3^3.
x^3 + 1/x^3 + 3(x + 1/x) = 27
x^3 + 1/x^3 + 3(3) = 27
x^3 + 1/x^3 + 9 = 27
x^3 + 1/x^3 = 27 - 9
x^3 + 1/x^3 = 18. ------------------- (1)
Given x^2 + 1/x^2 = 7
We know that (x - 1/x)^2 = x^2 + 1/x^2 - 2 * 1/x
= x^2 + 1/x^2 - 2
= 7 - 2
= 5.
Then (x - 1/x) = root 5. --------------- (2)
.
From (1) & (2),
The value of x^3 + 1/x^3 = 18.
The value of x - 1/x = root 5.
Hope this helps!
Answered by
8
x^2 + 1
_______. = (x + 1/x)^2 = x^2 + 1/x^2 + 2
x ^ 2 + 2
= 7 + 2 = 9
(x + 1 )
______
x = 3.
, we get
*************
(x + 1/x)^3 = 3^3.
x^3 + 1
______
x^3 + 3(x + 1/x). = 27
*************************************
x^3 + 1
______
x^3 + 3(3) = 27
**********************
x^3 + 1/x^3 + 9 = 27
x^3 + 1
________
x^3. = 27 - 9
x^3 + 1/x^3 = 18.
**********************
and x^2 + 1/x^2 = 7
(x - 1/x)^2 = x^2 + 1/x^2 - 2 * 1/x
= x^2 + 1/x^2 - 2
= 7 - 2
= 5.
------------------------------------
.
The value of x^3 + 1/x^3 = 18.
The value of x - 1/x = root 5.
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