MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
13 views
Find all pairs of positive real numbers such that $a^{3}+b^{3}+1=3 a b$.
| 13 views

0 like 0 dislike
Applying AM-GM to $a^{3}+b^{3}+1$, we get that
$$a^{3}+b^{3}+1 \geq 3 \sqrt[3]{a^{3} \times b^{3} \times 1}=3 a b .$$
Hence, we are in the equality case, and can conclude that $a=b=1 . \square$
by Diamond (75,914 points)

0 like 0 dislike