Question

Please see attached

a=2ab
b=sqrt(a-b)
c=b^2-2a

so

sqrt(a-b)^2-4(2ab)(b^2-2a)=0?????

Answer 1

The roots of a quadratic are = when the discriminant is zero
\[ ax^2+bx+c=0 \] has equal roots
if \[b^2-4ac=0\]

Answer 2

right, are my a b and c terms correct??

Answer 3

looks good.
don't have to take the square root though (sqrt(0)= 0 )

Answer 4

and of course (sqrt(a-b))^2 is a-b

Answer 5

right, and would 4(2ab)(b^2-2a)= 8ab(b^2-2a)

Answer 6

yes, but after that I don't see any nice simplification.

Answer 7

8ab^3-16a??

Answer 8

for the discriminant I get
\[a-b-8ab^3+16a^2b \]

Answer 9

is that simplified?

Answer 10

It is as simple as you can make it.

Answer 11

Is this the answer to your question?

Answer 12

no, I need t a relationship between a and b

Answer 13

@phi, what is the relationship???

Answer 14

my text just gave what you wrote as the answer.

Answer 15

OK, because I did not see anything except very ugly expressions.

Answer 16

huh?