If a≠b, and a2/(a-b)=b, which of the following could be a?

[Max@Math Revolution]

[GMAT math practice question]

If a≠b, and $$\frac{a^2}{\left(a-b\right)}=b$$ , which of the following could be a?

A. -1
B. 0
C. 1
D. 2
E. a does not exist

[DrMaths]

a2/(a-b)=b
a2 = b(a-b)
a2 -ba +b2 = 0
which can not be factorised, so a does not exist

[Max@Math Revolution]

=>
a^2/(a-b)=b
=> a^2=b(a-b)
=> a^2=ab - b^2
=> a^2 - ab + b^2 = 0
Since a≠b, one of a and b is not zero.
If a ≠ 0 or b ≠ 0, a^2 - ab + b^2 cannot be zero for the following reason:
a^2 - ab + b^2 = a^2 - 2a(b/2) + b^2 = a2 - 2a(b/2) + b^2/3 + (3/4)b^2
= ( a - b/2)^2 + (3/4)b^2 > 0
Thus, there is no pair of real numbers (a,b) satisfying the equation a^2 - ab + b^2 = 0.

Therefore, a cannot exist, and the answer is E.
Answer: E