Question

Q26. Prove that 4-3√2 is an irrational given that √2 irrational​

Answer 1

Answer:

let us assume 4-3√2 is rational hence it can be written as

4-3√2=p/q------->(1)(where p and q are co prime integers and q≠0)

subtracting 4 from both sides in eq(1)

-4+4-3√2=p/q-4

-3√2=p-4q/q

dividing both side by -3

√2=-(p-4q/3q)

here ,

-(p-4q/3q) is clearly rational but given that √2 is rational hence, it contradicts our assumption that 4-3√2 is rational

hence,It is irrational