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# Algebra

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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

#1
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Compute a + 5b.

Hello Guest!

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

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

$$a=60$$

$$b=\dfrac{1080}{60^2}$$

$$b=\dfrac{3}{10}$$

$$a+5b=61.5$$

!

Sep 2, 2021