If x^2 - 10x + 1=0 then x^4 + 1/x^4 = ..... ?

Answer 1

x^2-10x+1=0
=>x^2+1=10x
=> x+1/x=10 [dividing all the terms by x]
Now,X^2+1/x^2
=(x+1/x)^2-2*x*1/x
=(10)^2-2 [Putting the value of x+1/x]
=98
Therefore,x^4+1/x^4
=(x^2+1/x^2)^2-2x^2*1/x^2
=(98)^2-2
9604-2
=9602 ans

Answer 2

x1= (10+(100-4)^1/2)/2 or x2= (10-(100-4)^1/2)/2
then x1 = 5+2(6)^1/2
x2 = 5-2(6)^1/2

Considering x1
x^4 + 1/x^4 = (x^2)^2 + (1/x^2)^2
= (x^2 - 1/x^2)^2 + 2
= ((x + 1/x) (x - 1/x))^2 + 2
= (10 * 4 * (6)^1/2)^2 + 2
= 9602

Similarly considering x2 we get the value 9602

Answer 3

x^2 - 10x + 1=0
x^2 + 1 =10x

x +1/x =10

(x+1/x)^2 =10^2 -----(both side power by 2)
(x+1/x)^2=100
(x^2+2(x(1/x))+1/x^2) = 100
(x^2+2(1)+1/x^2) = 100
x^2+2+1/x^2=100
X^2+1/x^2=100-2
X^2+1/x^2=98

(x^2+1/x^2)^2 = (98)^2 ----(once again both side power by 2)
(x^2+1/x^2)(x^2+1/x^2) = (98)^2
(x^4 + 2(x^2(1/x^2))+1/x^4) =9604
(x^4 + 2(1)+1/x^4) =9604
(x^4 + 2+1/x^4) =9604

x^4+1/x^4 = 9604 - 2

The answer is
x^4+1/x^4 = 9602

Answer 4

Do your own homework.

Answer 5

this equtation can't have real roots