1) E(x) = [tex] x^{2} - 8x - 7[/tex]
E(-3) = [tex] -3^{2} [/tex] - 8 * (-3) +7
= 9+24+7=40
2) |x| * (2x -7 ) < 0
Daca rezolvam in N , prima conditie : x>0 (numar natural)
2x * |x| - 7* |x| <0
2*[tex] x^{2} [/tex] < 7x
0<x<[tex] \frac{7}{2} [/tex]
X trebuie sa fie in acel interval , rezulta x poate fi 1, 2 sau 3
3) [tex] \frac{x}{2 \sqrt{3}- \sqrt{2} } [/tex] = [tex] \frac{2 \sqrt{3} + \sqrt{2} }{5} [/tex]
Inmultumesc pe diagonala :
5* x = (2[tex] \sqrt{3} + \sqrt{2} [/tex] ) * ( [tex]2 \sqrt{3} - \sqrt{2} [/tex] )
Folosesc formula : (a+b)(a-b) = [tex] a^{2} - b^{2} [/tex]
5x = 12 - 2 = 10
x = 2
