Question

решить уравнение √(26+5x)-4-x=0

Answer 1

√(26+5x) - 4 - x = 0
(√(26+5x))² = (x+4)²
26+5x = x² + 8x + 16
x² + 3x - 10 = 0
D = 9 + 40 = 49
x1,2 = -3-+7/2
x1 = -5     x2 = 2
проверка:
1) √26+5*(-5) - 4 - (-5) = 0
√26-25 - 4 + 5 = 0
1 - 1 = 0
0 = 0

2) √26+5*2 - 4 - 2 = 0
√26+10 - 6 = 0
√36 - 6 = 0
6 - 6 = 0
0 = 0
ответь: (-5;2)

Answer 2

$\sqrt{26+5x} -4-x=0\\ \sqrt{26+5x}=x+4\\26+5x=(x+4)^2\\26+5x=x^2+16+8x\\-x^2+8x-5x+26-16=0\\-x^2+3x+10=0\\x^2-3x-10=0\\D=9+40=49\\ \sqrt{D} =7\\ x_{1} = \frac{3+7}{2} =5\\ x_{2} = \frac{3-7}{2} =-2 \\ \\ x+4 \geq 0\\x \geq -4$

$x=5,x=-2$