prove that 2 minus root 5 is an irrational number
Answers
hey dude !!!
=>> 2-√5 be a rational number
2-√5 = p/q (where p&q is a coprime intgers and q is not equal to 0 )
-√5 = p/2q
[√5 = -p/2q ]------------(1)
-p/2q = rational number. ( bcoz p & q are co prime ) --------------(2)
from (1)&(2)
√5 = rational number
which is not possible...
therefore our supposition of assuming 2-√5 was wrong ...
therefore it's irrational number
HENCE PROVED
hope this helps you ^_^
Step-by-step explanation:
Let 2-√5 is rational number so
2-√5 = p/q
Where q≠0 and p and q is coprime and we also known that 2 is rational no.
Now
√5 =-(p/q-2)
√5 = 2-p/q
Taking l.c.m we get
√5 = 2q-p/q
As we know that root 5is irrational no and how a irrational no.can be equal to a rational no. So here is a contraction.Hence
2-√5 is a irrational no.