Question

if x4+1/x4 = 198 find
(a) x2+1/x2
(b) x+1/x​

Answer 1

Answer:

Given x^4 + 1/x^4 = 23

(x^2 + 1/x^2)^2 - 2 = 23

(x^2 + 1/x^2)^2 = 25

x^2 + 1/x^2 = 5

(x + 1/x)^2 - 2 = 5

(x + 1/x)^2 = 7

(x - 1/x))^2 + 4 = 7

(x - 1/x)^2 = 3

Answer 2

Step-by-step explanation:

x4+1/x4 = 198

(a) (x^2 +1/x^2 )^2 = ( x^4+1/x^4) - 2

= 198 - 2 = 196

x^2+1/x^2 = sq.root 196 =14 Ans.

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

=14+2 =16

Therefore, x+1/x + sq.root 16 =4 Ans.