Răspuns:
Explicație pas cu pas:
[tex]t^4 + a^4 = a^2b^2+a^2c^2+b^2c^2 + a^4 = (a^2b^2+a^4)+(a^2c^2+b^2c^2)=\\=a^2(b^2+a^2)+c^2(a^2+b^2)=(a^2+b^2)(a^2+c^2)\\\texttt{Analog: }\\t^4+b^4 = (b^2+a^2)(b^2+c^2)\\t^4+c^4 = (c^2+a^2)(c^2+b^2)\\\texttt{Asadar:}\\\sqrt{(t^4+a^2)(t^4+b^2)(t^4+c^2)} = \sqrt{(a^2+b^2)^2\cdot(b^2+c^2)^2\cdot(a^2+c^2)^2}=\\=(a^2+b^2)\cdot (b^2+c^2)\cdot (c^2+a^2)\in\mathbb{Q}[/tex]
