Question

помогите решить ирациональное уравнение
а)√x+2=3
б)√x^2-1=2
в)√4x^2+5x-2=2

Answer 1

А)
$\sqrt{x} = 3 - 2 \\ \sqrt{x} = 1 \\ x = 1 \\ \sqrt{1} + 2 = 3 \\ 3 = 3 \\ x = 1$
Б)
$|x| - 1 = 3 \\ |x| = 3 + 1 \\ |x| = 4 \\ x = 4 \\ x = - 4 \\ x1 = - 4 \\ x2 = 4$
В)
$2 \times |x| + 5x - 2 = 2 \\ 2 \times |x| + 5x = 2 + 2 \\ 2 \times |x| + 5x = 4 \\ 2x + 5x = 4 \\ x \geqslant 0 \\ 2 \times ( - x) + 5x = 4 \\ x < 0 \\ x = \frac{4}{7} \\ x \geqslant 0 \\ x = \frac{4}{3} \\ x < 0 \\ x = \frac{4}{7}$