All Questions

Consider the quartic system in four variables $a,b,c,d\in\mathbb R$: $$-(c^2-d^2)(a^2-b^2)=2(ad-bc)(bd+ac).$$ Does this system admit rational solution with $$abcd(c^2-d^2)(a^2-b^2)(a^2-c^2)(b^2-d^2)\...