Question

Решите неравенства (1-√5)(x-3)<0

Answer 1

Ответ:

$( 1- \sqrt{5} )(x - 3) < 0 \\ x - 3 > 0 \\ x > 3$

Answer 2

To solve the inequality (1-√5)(x-3) < 0, follow these steps:

Step 1: Find the critical points. Set the expression inside the parentheses to zero and solve for x:

1 - √5 = 0 √5 = 1 No solution since the square root of 5 is not equal to 1.

x - 3 = 0 x = 3

Step 2: Create a number line. On the number line, mark the critical point x = 3.

------------------|-----------------|------------------- x < 3 x = 3 x > 3

Step 3: Test intervals. Choose a test point from each interval created by the critical points and plug it into the original inequality to determine the sign of the expression:

Test point x = 0 (interval x < 3): (1 - √5)(0 - 3) = (1 - √5)(-3) ≈ -7.07 < 0 (negative)

Test point x = 4 (interval x > 3): (1 - √5)(4 - 3) = (1 - √5)(1) ≈ -0.24 < 0 (negative)

Step 4: Determine the solution. The solution to the inequality is the interval where the expression (1 - √5)(x - 3) is negative:

x < 3 or x > 3

So, the solution to the inequality is x < 3 or x > 3.