Question

If x² − 8x + 1 = 0, find `x^2+1/x^2`.

Answer 1

x² − 8x + 1 = 0

Dividing the equation by x:

`x^2/x - (8x)/x + 1/x = 0`

`x - 8+1/x = 0`

`∴x + 1/x = 8`

Thus,

`8^2 = x^2 + 1/x^2 + 2`   ...`["Using"  (x+1/x^2)=x^2+1/x^2+2]`

`64 = x^2 + 1/x^2 + 2`

∴ `x^2 + 1/x^2 + 2` = 64 − 2

∴ `x^2 + 1/x^2 + 2 = 62`