Question

$Daca -2 \leq b \leq -1$, sa se resolve ecuatia :
$\sqrt{ (b+1)^{2} } - \sqrt{ (b+2)^{2} } + \sqrt{ ( 3-2b)^{2} } = \sqrt{ (b-3)^{2} }$

Answer 1

Din relatia de mai sus

=> | b + 1 | - | b + 2 | + | 3 - 2b | = | b - 3 |

Dar stim ca -2 ≤ b ≤ -1

deci: -b - 1 - b - 2 + | 3 - 2b | = -b + 3

-2b - 3 + | 3 - 2b | = -b + 3
-3 + | 3 - 2b | = b + 3
|3 - 2b| = b + 6

Deci avem 2 cazuri:

Cazul 1:
3 - 2b = b + 6 => -3 = 3b => b = -1

Cazul 2:
-3 + 2b = b + 6 => -9 = -b => b = 9

=> b ∈ { 1, 9}