Math Counts 5

Algebra Level 2

If A and B are real numbers such as a + b = a - b and a ≠ b, what is a value of A ² b + a + b − a b ² a − b \frac{A²b+a+b-ab²}{a-b} clear veiw A²b+a+b-ab²/a-b


The answer is 1.

Eric Zhu by Eric Zhu , 15, USA

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1 solution

Tom Engelsman
Oct 31, 2018

If the above expression is interpreted as:

a 2 b + a + b − a b 2 a − b \frac{a^{2}b + a + b - ab^{2}}{a-b} (i)

and if a + b = a − b a+b = a-b is satisfied for a , b ∈ R , a ≠ b a,b \in \mathbb{R}, a \neq b , then b = 0 b=0 and (i) equals a a = 1 . \frac{a}{a} = \boxed{1}.

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