Question

3. Prove that v3+V2 is an irrational.​

Answer 1

Answer:

Let us consider v3+V2 be rational number.

v3+V2 = p/q,. where q#0

v3 = (p/q) -√2

square on both side

(v3)² = p²/q²+2-2(p/q)(√2)

3 = p²/q²+2-(2√2p)/q

(2√2p)/q = p²/q²+2-3

(2√2p)/q = p²/q²-1

(2√2p)/q = (p²-q²)/q²

2√2 = (p²-q²)/pq

√2 = (p²-q²)/2pq

√2 is irrational number and (p²-q²)/2pq is rational number

LHS #RHS

Our assumption is wrong.

v3+V2 is an irrational.