Question

X^2-3x+1=0 then X^4+1/X^4=?

Answer 1

If x^2+x-1=0, then what is x^4+1/x^4?

x^2 + x - 1 = 0 ;

x^2 + x = 1 ;

x(x+1) = 1;

It tells that x is a non zero quantity, because if x=0, above equation(question) does not satisfy.

If x != 0 ;

we can divide mentioned equation by x.

(x^2 + x - 1)/x = 0/x;

x + 1 - 1/x = 0;

x - 1/x = -1;

Now square both side:

x^2 - 2.x.(1/x) + 1/x^2 = 1;

x^2 - 2 + 1/x^2 = 1;

x^2 + 1/x^2 = 3;

Again square both side:

x^4 +2.x^2.(1/x^2) +1/x^4 = 9;

x^4 + 2 + 1/x^4 = 9;

x^4 + 1/x^4 = 7;

Ans = 7.