ifx+inverse of x=4,calculate( x^6+1)/x^5+x^4?

Answer 1

x+(1/x) = 4 find (x^6+1)/x^5+(x^4)
squaring
x^2+(1/x^2) = 16 - 2=12 ---(1)

[x+(1/x)]^3 = x^3 +1/x^3 + 3 [x+(1/x)]
64 = x^3 +1/x^3 + 12
x^3 +1/x^3 = - 52
(x^6 +1) = - 52 x^3
multiply by (1)
(x^6 +1) (x^2+1/x^2) = - 52 x^3 (x^2+1/x^2) = -52 [x^5+x^4]

(x^6 +1) (12) = -52 [x^5+x^4]

(x^6 +1) / [x^5+x^4] = -52/12 = - 13/3

Answer 2

I think you mean-:

x + (1 / x) = 4

3.729 + (1/3.729) = 3.997 (near enough 4)

So now-:

x^6 + 1 / x^5 + x^4

3.729^6 + 1 / 3.729^5 + 3.729^4 = 2.942 (to 4sf)

Answer 3

Please explain "i f x"