Question

solve the equation for x by completing the square.
x² = kx + 1

Answer 1

\[\Large x^2-kx-1=0\]

\[\LARGE \Delta=b^2-4ac\]
\[\LARGE \Delta=(-k)^2-4\cdot (-1)\]
\[\LARGE \Delta=k^2+4\]

Now...

if:
\[\LARGE \Delta>0 \quad \longrightarrow \text{two solutions}\]
\[\LARGE \Delta=0 \quad \longrightarrow \text{one solution}\]
\[\LARGE \Delta<0 \quad \longrightarrow \text{no solution}\]

In our case we have ... ??

Answer 2

we have two solutions