Question

solve for x: 9sec^2(x/7)=3

Answer 1

\[9\sec^2\left(\frac{x}{7}\right)=3\\
\sec^2\left(\frac{x}{7}\right)=\frac{1}{3}\]
Do you know the details of the range of the secant function? Basically, \(\sec x\ge1\) or \(\sec x\le-1\), depending on the value of \(x\).

\(\dfrac{1}{3}\) lies betwen \(-1\) and \(1\), so there are no real solutions.