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Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673.  Find a - b.

 Jan 1, 2023
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Find a - b.

 

Hello Guest!

 

\(a^3 + 3ab^2 = 679\\ \underline{a^3 - 3ab^2 = 673}\\ 2a^3=1352\\ a^3=676\\ a=\sqrt[3]{676}=8,7638...\)

\(b=\sqrt{\frac{a^3-673}{3a}}\\ b=\sqrt{\frac{676-673}{3\cdot \sqrt[3]{676}}}\\ b=\sqrt{\frac{1}{\sqrt[3]{676}}}\\ \color{blue}a-b=\sqrt[3]{676}-\sqrt{\frac{1}{\sqrt[3]{676}}}=8.4388297647395448\\\)

laugh  !

a=8,776382955329128

b=0,3375531905895829

 Jan 1, 2023

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