Question

If $x^4-79x^2+1=0$then the value of $x+x^{-1}$ can be;

• A. 9
• B. 5
• C. 7
• D. 8

Answer 1

Answer:

A. 9

$x^4-79x^2+1=0$

divide the equation with $x^2$

$x^4/x^2-79x^2/x^2+1/x^2=0$

$x^2-79+1/x^2=0$

$x^2+1/x^2=79$

we have ,

If $x +1/x=k$then$x^2+1/x^2=k^2-2$

So here,

$k^2-2=79$

$k^2=81$

$k=9$

$x+x^{-1}=x+1/x=9$