prove that (2-7√3) is an irrational number where √3 is irrational
Answers
Answered by
5
Step-by-step explanation:
Let us assume in contradiction that 2√3-7 is rational number. Let 2√3-7 =a/b where a and b are co-primes. ... 2√3-7 is irrational number
Answered by
20
Step-by-step explanation:
Solution:
If possible, let be rational and let its simplest form be ,where a and b are integers and b≠0
Then,
⇛ =
⇛ = - 2
⇛ = ( - 2)
⇛ = ()... i
Now, is rational
⇛ is rational
⇛ () is rational (∵ difference of rationals is rational)
⇛ is rational [from (i)]
- But, it is given that is irrational.
- Thus, we arrive at a contradiction.
- Since the contradiction arises by assuming that () is rational
- Hence, () is irrational.
Similar questions
English,
2 hours ago
Math,
2 hours ago
English,
7 months ago
English,
7 months ago
Social Sciences,
7 months ago