if a=root 3 - root 2 ÷ root 3 + root 2 of b = root 3 + root 2 ÷ root 3 - root 2 find a square + b square = 5ab

Answer 1

a = (√3-√2)/(√3+√2)
b = (√3+√2)/(√3-√2)

Clearly ab=1

Doing the squares directly is a bit cumbersome, so let's rationalize the denominators:

a = (√3-√2)^2 = 5-2√6
b = (√3+√2)^2 = 5+2√6

Now we can take

a^2 = 49-20√6
b^2 = 49+20√6
a^2+b^2 = 98

Not sure that 98 = 5*1