Question

Prove that 2V3 - V5 is an irrational number.​

Answer 1

Answer:

Lets assume that 2V3-V5 is rational

we can find 2 integers a and b (b not equal to zero ) such that 2V3-V5=a/b

now

2V3=a/b+V5

2V3=a+V5b/b

V3=a+V5b/b/2

V3=(a+V5b)2/b

(a+V5b)2/b is rational and therefore V3 is rational

But this contradicts the fact that V3 is irrational

Therefore 2V3-V5 is rational.

Step-by-step explanation:

Answer 2

Answer:

V5 = -a + 2V3b /b

It's an irrational number

Step-by-step explanation:

2V3- V5 = a/ b

- V5= a/ b- 2V3

V5= - a + 2✓3b/ b