Question

find the value of (a+b) if 3+√2/3-√2=a+b√2​

Answer 1

if your question is, a & b are rational number,

3+(√2)13−(√2)=3+(√2)∗−23

<=>a=3,b=−23

if your question is, (without saying a, b are rational )

3+(√23)−(√2)=3+(√2)∗((√13)−1)

one solution of a and b is

a=3,b=((√13)−1)

I said “one solution” because anything that satisfy LHS = a+b(√2) can be a solution such as

a = 1, b = ((√13)−1)+(√2)

If it is 3+(√2)3−(√2)

then 3+(√2)3−(√2)=3+(√2)3−(√2)∗3+(√2)3+(√2)=(3+(√2))232−(√2)2

= (9+2+2∗3∗(√2)9−2

= (11+6∗(√2)7

a = 117

b = 67 ...