Question

SUBIECTUL 2 EXERCITIUL 2
E URGENT DAU CORONITA

15f4ecd8976bae5eb619d9e4f654e128.pdf

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Răspuns:

x₁ = 1  ; x₂ = 1/2  ; x₃ = 3/2

Explicație pas cu pas:

x ο y = 2xy - 2x -2y +3

a) 2020 ο 1  = 1  ??

2020 ο 1 = 2·2020·1 - 2·2020 - 2·1 + 3 =

= 4040 - 4040 - 2 +3 = 3-2 = 1

b) x ο y = 2·(x-1)·(y-1)+1  ??

x ο y = 2xy - 2x -2y +3 = 2x·(y-1) - 2y + 2 +1 =

= 2x·(y-1) - 2·(y-1) + 1 = (y-1)·(2x-2) + 1 = 2·(x-1)·(y-1) + 1

c) (x ο x) ο x = x  => x = ??

x ο x = 2x·x - 2x - 2x + 3 = 2x² - 4x + 3

(x ο x) ο x = (2x²-4x+3) ο x =

= 2·(2x²-4x+3)·x - 2·(2x²-4x+3) - 2x + 3 =

= (4x²-8x+6)·x - (4x²-8x+6) - 2x +3 =

= 4x³-8x²+6x - 4x²+8x-6-2x+3 =

= 4x³-12x²+12x-3  =>

4x³-12x²+12x-3 = x  <=>

4x³-12x²+11x-3 = 0

x₁ = 1    (4·1³-12·1²+11·1-3 = 4-12+11-3 = 15-15=0)

4x³-12x²+11x-3   :  (x-1)  = 4x²-8x+3

-4x³+4x²

_______

  /   -8x²+11x-3

       8x²-8x

      ________

       /       3x-3

              -3x+3

             ______

                /     /

4x²-8x+3 = 0   ; a = 4  ; b = -8  ; c = 3

Δ = b²-4ac = (-8)²-4·4·3 = 64 - 48 = 16

√Δ = √16 = 4

=> x₂,₃ = (-b ±√Δ)/2a = (8±4)/8  =>

x₂ = (8-4)/8 = 4/8 = 1/2

x₃ = (8+4)/8 = 12/8 = 3/2

Solutii : x₁ = 1  ; x₂ = 1/2  ; x₃ = 3/2