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