Question

E(x)=(2x+3)^2-(x-6)^2-3x(x+8)+10
Arata ca E(x)=-17 pentru orice x numar real

Answer 1

$E(x)=(2x+3)^2-(x-6)^2-3x(x+8)+10 = 4 {x}^{2} + 12x + 9 - ( {x}^{2} - 12x + 36) - (3{x}^{2} + 24x) + 10 = 4 {x}^{2} + 12x + 9 - {x}^{2} + 12x - 36 - 3{x}^{2} - 24x + 10 = (4 {x}^{2} - 4 {x}^{2}) + (24x - 24x) + (19 - 36) = \bf - 17$

q.e.d.