Math, asked by kush9486, 5 months ago

Show that 2√3 + 5 is an irrational number.​

Answers

Answered by MANAvRaja1245
18

Step-by-step explanation:

therefore it can be written in form of a and b where a and b are co-prime numbers. 5a/b is rational number as it is of the form p/q which is a rational number. but we know that √3 is irrational number so our assumption is wrong. 2√3/5 is irrational.01-Jun

Answered by Anonymous
6

Answer:

Let x=2−35 be a rational number.</p><p></p><p></p><p>35=2−x</p><p></p><p></p><p>5=32−x</p><p></p><p></p><p>Since x is rational, 2-x is rational and hence 32−x is also rational number</p><p></p><p></p><p>⇒5 is a rational numbers, which is a contradiction.</p><p></p><p></p><p>Hence 2−35 must be an irrational number.</p><p></p><p>

Let x=2−3

5

be a rational number.

3

5

=2−x

5

=

3

2−x

Since x is rational, 2-x is rational and hence

3

2−x

is also rational number

5

is a rational numbers, which is a contradiction.

Hence 2−3

5

must be an irrational number.

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