prove that 3 + 2 root 5 is irrational given that root 5 is irrational
Answers
Step-by-step explanation:
Hey!! mate nice to meet you
this is your answer
HOPE IT HELP YOU!!!!!!!!!!!!!!!
=>3+2√5
Let, 3+2√5 be rational
=> 3+2√5 = p/q (where p and q are co-prime & q is not equal to 0)
3+2√5 = p/q
squaring both sides,
(3+2√5)^2 = (p/q)^2
9+4×5 = p^2/q^2
29 = p^2/q^2
29×q^2 = p^2 ..............................................................eq.1
=> the above eq.1 shows that p^2 is factor of 29
=> p is also factor of 29
p= 29m (where m is some integer)................................eq.2
3+2√5 = p/q
from eq.2 we get,
3+2√5 = 29m/q
squaring both sides,
9+4×5 = 841m^2/ q^2
29 = 841m^2/q^2
q^2 = 841m^2/29
q^2 = 29m^2...............................................................eq.3
=> eq.3 shows that q^2 is also a factor of 29
but co-prime number have no factors
=> 3+2√5 is an irrational number.
PROVED
PLZ MADE ME BRILLIANT
___________________THANKYOU__________________