Let me give a hint. Note it's suspicious that the equations we're given all look very similar. In fact that means that if we set $f(x) = x^4 + x^2 + k\cdot x + 64$, then actually $a$, $b$, $c$, and $d$ are all roots of $f(x)$.

This means that we can take advantage of Vieta's theorem for a degree four, meaning that using Vieta's we should have information about:

• $a+b+c+d$ (the sum of the roots)
• $ab+ac+ad+bc+bd+cd$ (the sum of pairs of roots)
• etc.

How do these expressions relate to $a^2+b^2+c^2+d^2$?

Hope this helps, let us know if you have any additional questions.