Question 62
Is it true that for any real numbers $a$, $b$, $c$ and $d$ satisfying $a^2 + b^2 + (a-b)^2 = c^2 + d^2 + (c-d)^2$ also the equality
a)
$$
a^3 + b^3 + (a-b)^3 = c^3 + d^3 + (c-d)^3
$$
b)
$$
a^4 + b^4 + (a-b)^4 = c^4 + d^4 + (c-d)^4
$$
holds?
a)
$$
a^3 + b^3 + (a-b)^3 = c^3 + d^3 + (c-d)^3
$$
b)
$$
a^4 + b^4 + (a-b)^4 = c^4 + d^4 + (c-d)^4
$$
holds?