Question

Доказать,что число √(9-√43)^2 + √(6-√43)^2 - рациональное Помогите пожалуйста

Answer 1

/9-√43/+/6-√43/=9-√43+√43-6=3

Answer 2

Proof of the Rationality of √(9-√43)^2 + √(6-√43)^2

To prove that the given expression is rational, let's start by simplifying it step by step.

1. Simplify the expression: - √(9-√43)^2 + √(6-√43)^2 - = (9-√43) + (6-√43) (since √x^2 = |x|) - = 9 - √43 + 6 - √43 - = 15 - 2√43

2. Verify the rationality: - Now, we need to determine whether 15 - 2√43 is rational or not.

3. Definition of Rational Number: - A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to 0.

4. Conclusion: - Since 15 - 2√43 is in the form of a - b√c, where a, b, and c are rational numbers, it is an algebraic number. Therefore, 15 - 2√43 is irrational.

Based on the above steps, it can be concluded that the given expression √(9-√43)^2 + √(6-√43)^2 is irrational.