a.
( x + 1)² = -1
x² + 2x +1 = -1
x² + 2x + 2 = 0
DELTA = b² - 4ac = 2² - 4 * 1 * 2 = -4
DELTA < 0 donc pas de solutions
b.
(4x - 8)² = ( 3x + 1)²
16x² - 64x + 64 = 9x² + 6x +1
7x² - 70x + 63 = 0
x² - 10x +9 = 0
DELTA = 100 - 36 = 64
DELTA > 0 donc 2 solutions.
Soit x = ( b² - RACINE(DELTA) ) / 2a soit x = ( b² + RACINE(DELTA) ) / 2a
Donc x = (100 - 8) / 2 = 46 ou x = ( 100 + 8) / 2 = 54
c.
4x² + 4x + 1 = 121
4x² + 4x - 120 = 0
x² + x - 30 = 0
DELTA = 1 - 4 * (-30) = 121
DELTA > 0 donc deux solutions
x = ( 1 - 11) / 2 = -5 ou x =( 1 +11) / 2 = 6
