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IMAS 2012–2013 — Junior Division — Round 2 Question 5

IMAS · IMAS 2012–2013 — Junior Division — Round 2

Question 5

Let $a,b,c$ be rational numbers such that $c=-\frac{ab}{a+b}$. Which of the following expressions is correct?

$a+b+c=a^3+b^3+c^3$
$(a+b+c)^2=a^2+b^2+c^2$
$(a+b+2c)^2=a^2+b^2-4c^2$
$(a+b+c)^3=a^3+b^3+c^3$
$(a+b+c)(a^2+b^2+c^2)=a^3+b^3+c^3+abc$