Question

prove that 2+√3/5 is an irrational number​

Answer 1

Answer:

Answer

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.

Answer 2

Step-by-step explanation:

Let x=2−3

Let x=2−3 5

Let x=2−3 5

Let x=2−3 5 be a rational number.

Let x=2−3 5 be a rational number.3

Let x=2−3 5 be a rational number.3 5

Let x=2−3 5 be a rational number.3 5

Let x=2−3 5 be a rational number.3 5 =2−x

5

5

5 =

5 = 3

5 = 32−x

5 = 32−x

5 = 32−x

5 = 32−x Since x is rational, 2-x is rational and hence

5 = 32−x Since x is rational, 2-x is rational and hence 3

5 = 32−x Since x is rational, 2-x is rational and hence 32−x

5 = 32−x Since x is rational, 2-x is rational and hence 32−x

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5 is a rational numbers, which is a contradiction.

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5 is a rational numbers, which is a contradiction.Hence 2−3

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5 is a rational numbers, which is a contradiction.Hence 2−3 5

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5 is a rational numbers, which is a contradiction.Hence 2−3 5

5 = 32−x Since x is rational, 2-x is rational and hence 32−x is also rational number⇒ 5 is a rational numbers, which is a contradiction.Hence 2−3 5 must be an irrational number.