Question

(√3-2)x<√3-2 Подробно)

Answer 1

(√3-2)x<√3-2

√3-2<0

x<(√3-2)/(√3-2)

x>1

x€(1;+oo)

Answer 2

To solve the inequality (√3-2)x < √3-2, we'll need to isolate x on one side of the inequality. Let's break it down step by step:

Step 1: Distribute the x on the left side of the inequality: (√3 - 2)x < √3 - 2

Step 2: Now, we'll move the constant term (√3 - 2) to the right side by adding it to both sides of the inequality: (√3 - 2)x + 2 < √3

Step 3: Next, we want to isolate x. To do that, divide both sides of the inequality by (√3 - 2). However, there's one thing to note here. Since (√3 - 2) is negative (assuming x is real), dividing by a negative number will flip the inequality sign. So, we need to be careful:

(√3 - 2)x + 2 < √3

Divide both sides by (√3 - 2), remembering to flip the inequality sign: x < (√3) / (√3 - 2)

Now, we have the solution for x. Let's simplify (√3) / (√3 - 2):

To rationalize the denominator, we'll multiply both the numerator and denominator by (√3 + 2) (conjugate of (√3 - 2)):

(√3) / (√3 - 2) * (√3 + 2) / (√3 + 2)

Using the difference of squares (a^2 - b^2 = (a + b)(a - b)), the denominator simplifies:

= (√3 * (√3 + 2)) / ((√3)^2 - (2)^2) = (√3 * (√3 + 2)) / (3 - 4) = (√3 * (√3 + 2)) / (-1) = -√3 - 2

So, the inequality becomes:

x < -√3 - 2

That's the final solution. Any value of x that is less than -√3 - 2 will satisfy the original inequality (√3 - 2)x < √3 - 2.