Question

Prove that 3 + 2√5 is irrational.

Answer 1

Answer:

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Step-by-step explanation:

Let 3 + 2√5 be a rational number.  

Then the co-primes x and y of the given rational number where (y ≠ 0) is such that:  

3 + 2√5 = x/y  

Rearranging, we get,  

2√5 = (x/y) – 3  

√5 = 1/2[(x/y) – 3]  

Since x and y are integers, thus, 1/2[(x/y) – 3] is a rational number.  

Therefore, √5 is also a rational number. But this confronts the fact that √5 is irrational.  

Thus, our assumption that 3 + 2√5 is a rational number is wrong.  

Hence, 3 + 2√5 is irrational.

Answer 2

Answer:

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