Thread: Surds

Given that [a - 6 sqrt(5)] x [2 + b sqrt(5)] = -82, where a and b are rational numbers, find the possible values of a and b
[Ans = a = 4, b =3, or a = -45, b = -4/15]

I have expanded the expression to obtain
2a + sqrt 5 (ab-12) - 30 b = 82, but I don't know how to proceed to get simulataneous equations to solve for a and b.

Please help.
Thanks

Originally Posted by Drdj

Given that [a - 6 sqrt(5)] x [2 + b sqrt(5)] = -82, where a and b are rational numbers, find the possible values of a and b
[Ans = a = 4, b =3, or a = -45, b = -4/15]

I have expanded the expression to obtain
2a + sqrt 5 (ab-12) - 30 b = 82, but I don't know how to proceed to get simulataneous equations to solve for a and b.

Please help.
Thanks

We need to know that "a and b are rational numbers" in order to be certain that is not a rational number and so we can so we must have .