Question

prove that 5+√5 is an irrational number​

Answer 1

Answer:

let us assume to the contray that 5+√5 is rational then their exist co prime positive integers a and b such that 5+√5 =a/b

• 5+a/b= 3
• 5b+a/b = √5

√5 is rational (a,b are intgers and 5b+a/b is a rational number

this contradicts the fact that √5 is irrational .so our assumption is incorrect ,Hence 5+√5 is an irrational number.

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