Răspuns:
[tex] \sqrt{x + 2} + \sqrt{x - 7} = \sqrt{2x - 5} \\ (x + 2) + 2 \sqrt{(x + 2)(x - 7)} + (x - 7) = 2x - 5 \\ 2x - 5 + 2 \sqrt{ {x}^{2} - 7x + 2x - 14 } = 2x - 5 \\ 2x - 5 + 2 \sqrt{ {x}^{2} - 5x - 14} = 2x -5 \\ 2\sqrt{ {x}^{2} - 5x - 14} = 0 \\ 4( {x}^{2} - 5x - 14) = 0 \\ 4 {x}^{2} - 20x - 56 = 0 \\ delta = 400 - 4 \times 4( - 56) \\ = 400 + 16 \times 56 \\ 400 + 896 \\ = 1296 \\ x1 = \frac{20 + 36}{800} \frac{56}{800} \\ x2 = \frac{20 - 36}{800} = \frac{4}{800} [/tex]
