a and b are real numbers and satisfy a*b^2 = 27/5 and a^2*b = 1080. Compute a + 5b.
+1224 ab^2 = 27/5
(a^2)b = 1080
Multiply: \(a^3b^3 = 5832 \quad \rightarrow \quad ab=18\)
We know that \(a^2b = 1080\), so dividing gets a = 60 and b = 3/10.
a + 5b = 60 + 3/10 * 5 = 60 + 3/2 = 61.5
