Question

Daca E(x)=x la a 2-a -8x+7,atunci E(-3)=..?

Rezolvati in N inecuatia |x|·(2x-7)<0

Det. nr real x,care ferifica egalitatea :x supra 2√3-√2=2√3+√2 supra 5

Answer 1

1) E(x) = $x^{2} - 8x - 7$
E(-3) = $-3^{2}$ - 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*$x^{2}$ < 7x
0<x<$\frac{7}{2}$
X trebuie sa fie in acel interval , rezulta x poate fi 1, 2 sau 3

3) $\frac{x}{2 \sqrt{3}- \sqrt{2} }$ = $\frac{2 \sqrt{3} + \sqrt{2} }{5}$
Inmultumesc pe diagonala :
5* x = (2$\sqrt{3} + \sqrt{2}$ ) * ( $2 \sqrt{3} - \sqrt{2}$ )
Folosesc formula : (a+b)(a-b) = $a^{2} - b^{2}$
5x = 12 - 2 = 10
x = 2