Question

Решите неравенства (x-3)(x-1)<0​

Answer 1

Объяснение:

........................

Answer 2

(х-3)(х-1)<0

х^2-х-3х+3<0

х^2-4х+3<0

D=(-4)^2-4*1*3=16-12=4

x1=(4+2)/2=3

x2=(4-2)/2=1

Ответ:x€(1;3)

Answer 3

To solve the inequality $(x-3)(x-1) < 0$, we need to find the intervals where the expression $(x-3)(x-1)$ is negative.

Step 1: Find the critical points (where the expression equals zero) Set $(x-3)(x-1) = 0$ and solve for $x$: $(x-3)(x-1) = 0$ Either $x-3 = 0$ or $x-1 = 0$ Solving each equation separately:

1. $x-3 = 0 \Rightarrow x = 3$
2. $x-1 = 0 \Rightarrow x = 1$

Step 2: Create a sign chart A sign chart will help us determine the sign of $(x-3)(x-1)$ in different intervals:

• $(-\infty, 1)$
• $(1, 3)$
• $(3, +\infty)$

Step 3: Test a value in each interval to find the sign of the expression Pick a value in each interval and plug it into $(x-3)(x-1)$:

• For $x = 0$, $(0-3)(0-1) = 3 > 0$ (positive)
• For $x = 2$, $(2-3)(2-1) = -1 < 0$ (negative)
• For $x = 4$, $(4-3)(4-1) = 3 > 0$ (positive)

Step 4: Analyze the results The expression $(x-3)(x-1)$ is negative in the interval $(1, 3)$ since it equals a negative value for any $x$ in that interval.

Step 5: Write the solution The solution to the inequality is $1 < x < 3$, or in interval notation: $(1, 3)$. This means that any value of $x$ within the open interval (1, 3) will satisfy the inequality $(x-3)(x-1) < 0$.