a and b are real numbers and satisfy a*b^2 = 27/5 and a^2*b = 1080. Compute a + 5b.
+14995 Compute a + 5b.
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\(ab^2=\dfrac{27}{5}\\ a^2b=1080\\ b=\dfrac{1080}{a^2}\\ a\cdot (\dfrac{1080}{a^2})^2=\dfrac{27}{5}\)
\(\dfrac{1080^2}{a^3}=\dfrac{27}{5}\\ a=\sqrt[3]{\dfrac{5\cdot 1080^2}{27}}\)
\(a=60\)
\(b=\dfrac{1080}{60^2}\)
\(b=\dfrac{3}{10}\)
\(a+5b=61.5\)
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