Question

if (x+1/x) =√7 then find the value of x2+1/x2 and x4+1/x4​

Answer 1

Answer:

Given: x + 1/x = 7 Squaring on both sides ⇒ (x + 1/x )2 =(7)2 ⇒ x2 + ( 1/x)2 + 2(x)(1/x) = 49 [∵ (a+b)2= a2+b2 + 2ab] ⇒ x2 + 1/(x2) + 2 = 49 ⇒ x2 + 1/(x2) = 49 - 2 ∴ x2 + 1/(x2) = 47

Answer 2

Step-by-step explanation:

( x+ 1/x )2 =($\sqrt{7\\}$)2

x2 + 1/x2 + 2 = 7

x2 + 1/x2 = 7 - 2

               =5

x2 + 1/x2 = 5

( x2 + 1/x2 )2 = (5)2

x4 + 1/x4 + 2 = 25

x4 + 1/x4 = 25-2

               = 23

x4 + 1/x4 = 23