Question

√2x+1-√5-x=2
НАЙТИ X

Answer 1

$\sqrt{2x + 1} - \sqrt{5 - x} = 2 \\ \sqrt{2x + 1} - = 2 + \sqrt{5 - x} \\ 2x + 1 = 4 + 4 \sqrt{5 - x} + 5 - x \\ 2x + 1 = 9 + 4 \sqrt{5 - x} - x \\ - 4 \sqrt{5 - x} = 9 - x - 2x - 1 \\ - 4 \sqrt{5 - x} = 8 - 3x \\ 16(5 - x) = 64 - 48x + 9 {x}^{2} \\ 80 - 16x = 64 - 48x + 9 {x}^{2} \\ 80 - 16x - 64 + 48x - 9 {x}^{2} = 0 \\ 16 + 32x - 9 {x}^{2} = 0 \\ - 9 {x}^{2} + 32x + 16 = 0 \\ 9 {x}^{2} - 32x - 16 = 0 \\ d = {b}^{2} - 4ac \\ d = ( - 32) {}^{2} - 4 \times 9 \times ( -16) = 1024 -( - 576) = 1024 + 576 = 1600 \\ x12 = \frac{ - b + - \sqrt{d} }{2a} \\ x12 = \frac{32 + - 40}{18} = \\ \frac{32 - 40}{18} = - \frac{4}{9} \\ \frac{32 + 40}{18} = \frac{72}{18} = 4$
х=4