Math, asked by shubham2506, 11 months ago

4. Prove that: 2√3-4 is an irrational number, using the fact that √3 is an irrational number.

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Answered by Shubhanb
4

Step-by-step explanation:

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Answered by shkulsum3
1

To prove that 2√3 - 4 is an irrational number,

we can assume the opposite, that it is a rational number. Let's assume that it can be written as a ratio of two integers, a and b, such that a and b have no common factors other than 1 (i.e. they are in lowest terms). That is:

2√3 - 4 = a/b

Squaring both sides of the equation, we get:

(2√3 - 4)² = (a/b)²

4(3) + 16 - 8√3 = a²/b²

12 + 16 - 8√3 = a²/b²

28 = a²/b²

Now, let's substitute the fact that √3 is an irrational number. Since √3 is not equal to any fraction of integers,

we can assume that  a²/b² = 3:

28 = 3

This is a contradiction, because 28 is not equal to 3.

So, our assumption that 2√3 - 4 is a rational number is false.

Hence, we have proved that 2√3 - 4 is an irrational number.

Know more from the following links.

brainly.in/question/16766451

brainly.in/question/4211888

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