Question

Tìm x, biết

(x - 2)(x² + 2x + 4) + 2(x² - 4) - 5(x - 2) = 0

Answer 1

(x - 2)(x² + 2x + 4) + 2(x² - 4) - 5(x - 2) = 0

(x - 2)(x + 2)² + 2(x - 2)(x+2) - 5(x - 2) = 0

(x - 2)[(x+2)² + 2(x+2) - 5]= 0

(x - 2)[(x + 2)² + 2(x + 2) + 1 - 6] = 0

( x - 2)[(x + 2 + 1)² - 6] = 0

(x - 2)[(x + 3)² - 6] = 0

(x - 2)(x + 3 - \(\sqrt{6}\))(x + 3 + \(\sqrt{6}\)) = 0

TH1. x - 2 = 0 <=> x = 2

TH2. x + 3 - \(\sqrt{6}\) = 0 <=> x = \(\sqrt{6}-3\)

TH3. x + 3 + \(\sqrt{6}\) = 0 <=> x = \(-\sqrt{6}-3\)

S = {2; \(\sqrt{6}-3\); \(-\sqrt{6}-3\)}