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# a and b are real numbers

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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.

Mar 1, 2021

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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

Mar 1, 2021