Question

If `y = x + 1/x`, then write the equation `x^4 + x^3 -4x^2 +x +1 = 0` in terms of `y`?

Answer 1

`y+y^2-6=0`

Explanation:

`x^4 + x^3 -4x^2 +x +1=x^2(x^2+x-4+1/x+1/x^2) = x^2(y+y^2-6)=0`

but `x ne 0` so

`x^4 + x^3 -4x^2 +x +1=0 hArr y+y^2-6=0`