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a and b are real numbers and satisfy a*b^2 = 27/5 and a^2*b = 1080. Compute a + 5b.

 Sep 2, 2021
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Compute a + 5b.

 

Hello Guest!

 

\(ab^2=\dfrac{27}{5}\\ a^2b=1080\\ b=\dfrac{1080}{a^2}\\ a\cdot (\dfrac{1080}{a^2})^2=\dfrac{27}{5}\)

\(\dfrac{1080^2}{a^3}=\dfrac{27}{5}\\ a=\sqrt[3]{\dfrac{5\cdot 1080^2}{27}}\)

\(a=60\)

\(b=\dfrac{1080}{60^2}\)

\(b=\dfrac{3}{10}\)

 

\(a+5b=61.5\)

laugh  !

 Sep 2, 2021

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