Question

Решите графическое уравнение 2/х=х+1

Answer 1

$\frac{2}{x} = x + 1 \\ 2 = x(x + 1) \\ 2 = {x}^{2} + x \\ - {x}^{2} - x + 2 = 0 \\ {x}^{2} + x - 2 = 0 \\ d = {b}^{2} - 4ac = {1}^{2} - 4 \times 1 \times ( - 2) = 1 + 8 = 9 \\ x1 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 1 + 3}{2} = \frac{2}{2} = 1 \\ x2 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 1 - 3}{2} = \frac{ - 4}{2} = - 2$
Ответ: х1 = 1; х2 = -2

Answer 2

2
----=x+1 /x
x

2=x^2+x
x^2+x-2=0
D=1+2*2=5
x= -1+-корень5