Question

if x2+1/x2=14then x3+1/x3=?

Answer 1

2x+1/2x=14
2x+1=28
1=26x
1/26=x

3x+1/3x
3(1/26)+1/3/26
3+26/26*26/3
29/3
96.66

Answer 2

Here is your answer

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x^2 + 1/x^2 = 14

(x + 1/x)^2 -2.x.1/x = 14

(x + 1/x )^2 -2 = 14

(x + 1/x )^2 = 16

Now,
square root both sides, we get
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(x + 1/x) = 4

then,

x^3 + 1/x^3 = ( x + 1/x)^3 - 3.x.1/x(x + 1/x)

================================

x^2+ 1/x^2 = 14

(x + 1/x)^2 - 2(x) (1/x) = 14

(x + 1/x)^2 = 14+2

(x + 1/x)^2 = 16

x + 1/x = √16

x + 1/x = 4
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(x^3 + 1/x^3) = (x + 1/x)^3 - 3 (x.1/x) (x+1/x)

= 4^3 - 3(4)
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64 - 12

= 52

Hope it's helpful for you