Question

DAU 48+25 PUNCTE SI COROANA! Ajutațimă la 4 și 9. Se incepe asa ca at al doilea atasament, conditia e in primul atasament

Answer 1

4)

$a+b=95\\a-b=40\Rightarrow a=b+40\\b+40+b=95\Rightarrow 2b=55\Rightarrow b=\displaystyle\frac{55}{2}\\\displaystyle a=b+40=\frac{135}{2}$

9) a)

$\displaystyle F(x)=\frac{9x^4-6x^2+1}{3x^3-x}=\frac{(3x^2-1)^2}{x(3x^2-1)}\\C.E.\left \{ {{x\neq0} \atop {3x^2-1\neq0}} \right. \\F(x)=\frac{3x^2-1}{x}$

b)

$F(x)\in\mathbb{Z}\Rightarrow\displaystyle\frac{3x^2-1}{x}\in\mathbb{Z}\\\\x|(3x^2-1)\Rightarrow \left \{ {{x|3x^2} \atop {x|(-1)}} \right. \\x|3x^2 (A),\forall x\in\mathbb{Z}\\x|(-1)\Rightarrow x\in\{\pm1\}\\F(1)=2\in\mathnn{Z}\\F(-1)=-2\in\mathbb{Z}\\\matcal{S}=\{\pm1\}$