Question

Prove that 3 + 2√5 is irrational.

Answer 1

Step-by-step explanation:

Let us say 3 + 2√5 is rational.

Then the co-prime 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.

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Hence, we get that 3 + 2√5 is irrational.

Answer 2

Answer:

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