Question

Rezolvati , in multimea numerelor reale , ecuatia 2 (x+2)² - (3-x)² -4 = 2(x²+4) - (x-1)² .

Answer 1

2 (x+2)² - (3-x)² -4 = 2(x²+4) - (x-1)²

2 (x² + 4x + 4) - 9 + 6x - x² - 4 = 2x² + 8 - x² + 2x - 1

2x²  +8x + 8 - 9 + 6x - x² - 4 = x² + 2x + 7

x² + 14x - 5 = x² + 2x + 7

x² - x² + 14x - 2x - 5 - 7 = 0

0 + 12x - 12 = 0

12x - 12 = 0

12x = 12

x=1

Answer 2

2(x+2)²-(3-x)²-4 =2(x²+4)-(x-1)² 
2(x²+2·x·2+2²)-(3²-2·3·x+x²)-4=2·x²+2·4-(x²-2·x·1+1²)
2(x²+4x+4)-(9-6x+x²)-4=2x²+8-(x²-2x+1)
2x²+8x+8-9+6x-x²-4=2x²+8-x²+2x-1
14x-5=7+2x
14x-2x=7+5
12x=12
x=12:12
x=1