Question

√2x-√3=1,6 Иррациональное

Answer 1

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Answer 2

Um, it seems like there's a little confusion in your statement. I'll clarify the parts of your expression and help you understand it.

The expression you provided is: √(2x) - √3 = 1.6

To check if the value of x is irrational, we need to solve for x. The equation contains two square roots, and the sum of the square roots equals a rational number (1.6).

Let's solve the equation step by step:

1. Move √3 to the other side of the equation: √(2x) = 1.6 + √3

2. Isolate √(2x) by squaring both sides of the equation: (√(2x))^2 = (1.6 + √3)^2 2x = 2.56 + 3.2√3 + 3

3. Now, isolate x by dividing both sides by 2: x = (2.56 + 3.2√3 + 3) / 2

To determine if x is irrational, we need to check if the value of x obtained is rational or irrational. If the value contains an irrational part (√3 in this case), then x is irrational.

Let's calculate the value of x to determine if it's irrational:

x ≈ (2.56 + 3.2√3 + 3) / 2 ≈ (5.56 + 3.2√3) / 2

As you can see, the value of x contains the term √3, which is an irrational number. Therefore, the value of x is irrational.