conditie: 2x -1 ≥ 0 ; 2x ≥ 1 ; x ≥ 1 / 2
2 - x ≥ 0 ; 2 ≥ x
solutia , 1 / 2 ≤ x ≤ 2
rezolvare : daca ridicam la patrat :
√(2x-1)² = [ 2 - √(2-x)]²
2x -1 = 4 - 4√(2-x) + 2 - x
4√(2-x) = 7 -3x la patrat :
16(2 -x) = 49 - 42x + 9x²
9x² - 42x + 16x + 49 - 32 = 0
9x² - 26x + 17 =0 ; Δ =676 - 4·9·17= 64 ; √Δ=√64 = 8
x₁ = (26 - 8) / 18 = 18 /18 = 1 ≤ 2 ; deci solutie
x₂ = (26 + 8) / 18 = 34 /18 = 17 / 9 = 1,(8) ≤ 2 ; deci solutie
