Question

if x squared plus one upon x square equals to 14 find the value of x cube plus one upon x cube

Answer 1

x^2+1/x^2=14
(x+1/x)^2-2x*1/x=14
(x+1/x)^2-2=14
(x+1/x)^2=16
(x+1/x)=4
cubbing both the sides
x^3+1/x^3+3x^2*1/x+3x*1/x^2=64
x^3+1/x^3+3(x+1/x)=64
x^3+1/x^3+3*4=64
x^3+1/x^3=64-12
x^3+1/x^3=52

hope this helps:p

Answer 2

we know that 2*x*1/x = 2---(1)

x² + 1/x² =14
add bothsides 2 

x²+1/x² +2 = 14+2
x² +1/x² +2 *x*1/x = 16  from (1)
(x+1/x)² =16 ---(2)
x+1/x = 4 or -4

now 
if we x+1/x =4
i)x³ +1/x³ = (x+1/x) [ x²+1/x² -x*1/x]

= 4* [ 14 -1]
= 4* 13
=52
ii) if take x+1/x = -4
x³+1/x³ = (-4) [14 -1]
=(-4) *13
=-52