# If $\cos x + \cos y=1$ and $\cos x \cos y=1/4$, then find the general solutions for x and y

Squaring on both sides $$\cos^2 x + \cos^2 y + 2\cos x \cos y=1$$ I know w don’t generally square while finding general solutions, but I couldn’t see any other way $$\cos^2 x +\cos^2 y=1/2$$ I couldn’t solve further. How should I proceed?

• Finding two numbers given product and sum is equivalent to solving a quadratic equation... – dfnu Nov 20 '19 at 13:38
• Yeah, that works, didn’t think like that. Thanks! – Aditya Nov 20 '19 at 13:53

Can you solve for $$a, b$$
$$\cases{a+b=1\\ a b = \frac 14}$$ ?