Calculate $f(x)$ at a specific point Question:
Calculate $f(x) = \frac{49}{x^2} + x^2$ at points for which $\frac{7}{x}+x =3$
My attempt:-
I tried to find the value of $x$ and insert in $f(x)$
$$\frac{7}{x}+x =3$$
$$7+x^2 =3x$$
$$x^2 -3x + 7=0$$
$$x = \frac{3+\sqrt{9-7*4}}{2}$$
Now $x$ is coming out to be irrational and things get a lot more difficult from there. What should I do?

Make use of
$$
\left(\frac{7}{x}+x \right)^2=\frac{49}{x^2}+x^2+14
$$
i.e.
$$
3^2-14=\frac{49}{x^2}+x^2=-5
$$
