Question

Fie A multimea solutiilor reale ale ecuatiei -6x^2-x+2=0.Determinati multimea A in intersectie cu multimea -1/2 ; 1 . Cu explicatii

Answer 1

-6x² - x + 2 = 0 |·(-1) ⇔ 6x² + x - 2 = 0 ⇔ 6x² -3x + 4x -2  = 0 ⇔

⇔ 3x(2x - 1) +2(2x - 1) = 0 ⇔ (2x - 1)(3x+2) = 0

2x - 1 = 0 ⇔ 2x = 1 ⇔ x = 1/2

3x + 2 = 0  ⇔ 3x = -2 ⇔ x = -2/3

A = {-2/3,  1/2}

{-2/3,  1/2} ∩ {-1/2,  1} = ∅.