Question

prove that 1/2-√5/3 is irrational number

Answer 1

if possible let (1/2 - √5/3) be a rational number x
1/2-√5/3 => x
making denominator equal
(3-2√5)/6 => x
3-2√5 = 6x
3-6x = 2√5
2(1-2x)/2 = √5
1-2x = √5


since , x is rational number (by our supposition)
2x is also rational
1 is rational
and we know that , difference of 2 rationals is rational number
so, this tells us that √5 is also rational
but , √5 is irrational
thus , our supposition is wrong
so x is not rational ,
and x = 1/2 -√5/3
so, 1/2 - √5/3 is irrational

hope this helps

Answer 2

Step-by-step explanation:

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