Question

prove that one upon 2 minus under root 5 is an irrational number

Answer 1

Answer:

Step-by-step explanation:-----------

Let us assume on the contrary that 1/2-√5 is a rational no.

Then there exist two co-prime integers a and b such that --

1/2-√5 =a/b

-√5=a/b-1/2

(Now taking minus a as common)

√5=1/2-a/b

√5=b-2a/2b

( a,b are integers therefore b-2a/2 is rational)

As we know √5 is rational. So this contradicts the fact that √5 is irrational. And our assumption gets wrong,

Hence, 1/2-√5 is an irrational.

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Answer 2

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