<s>[INST] Find all real $x$ ,such $8x^3-20$ and $2x^5-2$ is perfect square 
Find all real numbers $x$,such 
  $$8x^3-20,2x^5-2$$  is  the perfect square of an integer

My idea: First we find the real number $x$ such $$8x^3-20,2x^5-2$$ is postive integer numbers,and second the real numbers such
$$8x^3-20=m^2,2x^5-2=n^5$$
How prove this all real numbers?
 [/INST] Hint.  If we have
$$8x^3-20=m^2\ ,\quad 2x^5-2=n^2$$
then
$$x^3=\frac{m^2+20}{8}\ ,\quad x^5=\frac{n^2+2}{2}\ .$$
Can you see how to obtain $x$ from these two equations?
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