Maths Olympiad Prep

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Algebra Difficulty 2.3 Junior Find the answer Canada

The operation a∇ba \nabla b is
defined by $a∇\$a\nabla b =
a+ba−b\dfrac{a+b}{a-b}forallintegers for all integers aand and bwith with a ≠\neq
b.Forexample,. For example, 2∇2\nabla 3 =
2+32−3\dfrac{2+3}{2-3} = -5.If. If 3∇3\nabla
b=-4,whatisthevalueof, what is the value of b$?

Pick one

Solution

Using the definition, $3∇\$3\nabla b =
3+b3−b$.\dfrac{3+b}{3-b}\$.

Assuming b≠3b \neq 3, the following
equations are equivalent: 3∇b=−43+b3−b=−43+b=−4(3−b)3+b=−12+4b15=3b\begin{align*} 3 \nabla b & = -4 \\ \dfrac{3+b}{3-b} & = -4 \\ 3+b & = -4(3-b) \\ 3+b & = -12 + 4b \\ 15 & = 3b\end{align*} and so $b
= 5$.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.