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$$\sqrt{x - a} + \sqrt{x - 5} = 0$$ then $$a$$ is a solution of
A sum of two non-negative square roots is 0 only if both are 0, so $$x = a$$ and $$x = 5$$, giving $$a = 5$$. Now $$5^2 - 6(5) + 5 = 0$$ and $$5^2 - 7(5) + 10 = 0$$. Also $$x^2 - x + 1 > 0$$ and $$x^2 + x + 1 > 0$$ hold for every real $$x$$, so 5 satisfies them too. Hence all four options a, b, c and d are correct.
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