Question

am nevoie de ajutor ​

Answer 1

Răspuns:

Explicație pas cu pas:

$x*y=x+y+x^{2} y^{2}$

a)

$1*2=1+2+1^{2} *2^{2}=3+4=7$

b)

$x*e=e*x=x => \\1)x*0=x+0+x^2*0^2=x\\2)0*x=0+x+0^2*x^2=x$

Din 1) si  2) => e=0  element neutru

c)

$(-2)*x\leq 3=> -2+x+(-2)^2*x^2\leq 3=>4x^2+x-2-3\leq 0=>4x^2+x-5\leq 0$

$4x^2+x-5=0 \\d=b^2-4*a*c=1^2-4*4*(-5)=1+80=81\\x_{1}=\frac{-b+\sqrt{d}}{2*a}=\frac{-1+\sqrt{81}}{2*4}=\frac{-1+9}{8}=\frac{8}{8}=1\\x_{2}=\frac{-b-\sqrt{d}}{2*a}=\frac{-1-\sqrt{81}}{2*4}=\frac{-1-9}{8}=\frac{-10}{8}=\frac{-5}{4}$

x                 |-∞                 $\frac{-5}{4}$           1                              +∞        

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$4x^{2}+x-5$ |-∞    ++++++   0 ------   0  +++++++++++++   +∞

x∈[$\frac{-5}{4}$;1]