Question

prove (2-3√5 ) is an irrational number​

Answer 1

HOPE YOU UNDERSTAND IT OF YES PLSS MARK AS BRAINLIST

Answer 2

let 2-3root5 be rational number

2-3root5 = a/b ( a and b are co prime )

root5 = a+2b/3b

root5 and a+2b/3b are rational numbers.

root5 = k/s ( k and s are co prime )

5 = k^2/s^2

5s^2 = k^2 .........1

k^2 is divisible by 5

k is also divisible by 5

k = 5c .............2

Pu5 equation 2 in 1

25 c^2 = 5 s^2

5c^2 = s^2

s^2 is divisible by 5

s is also divisible by 5

it contradict that s and k are co prime numbers. So, our supposition was wrong.

2-3root5 is an irrational number