Then multiply both sides by 3-√a. Expand the right hand side. Equate the whole number parts on each side to find a. Equate the coefficients of the √2 parts on each side to find b.
Apologies. What I said doesn't work because it turns out that √a is itself a multiple of √2 so, as you imply, it's not clear which are the whole number parts. Maybe someone else has a suggestion? Your answer is correct, a = 8 and b = 17 works.
Apologies. What I said doesn't work because it turns out that √a is itself a multiple of √2 so, as you imply, it's not clear which are the whole number parts. Maybe someone else has a suggestion? Your answer is correct, a = 8 and b = 17 works.
yes it works, but I have no clue why. anyone else?
Hi oufoufoufouf, Maybe I've missed some easy method. If not, then you are right, it is way beyond GCSE.
A hack would be be to note that * Both the numerator and right hand side are sqrt(2) surds, so the denominator must be (3-ksqrt(2)) as well, otherwise the surd parts won't match. * Also the only valid values for a are 5,6,7,8 otherwise the denominator is too large to match the integer part on the right or negative. 8 is the only value for a satisfying both and then you can get b.