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# algebra

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If  a + b = 7 and a^3 + b^3 = 44, what is the value of the sum 1/a + 1/b? Express your answer as a common fraction.

May 14, 2021

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+26213
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If  $$a + b = 7$$ and $$a^3 + b^3 = 44$$,
what is the value of the sum $$\dfrac{1}{a} + \dfrac{1}{b}$$?
$$\begin{array}{|rcll|} \hline (a+b)^3 &=& a^3+b^3+3ab(a+b) \quad | \quad a + b = 7,~a^3 + b^3 = 44 \\ 7^3 &=& 44 +21ab \\ 21ab &=& 343 - 44 \\ \mathbf{ ab } &=& \mathbf{ \dfrac{299}{21} } \\ \hline \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{a+b}{ab} \quad | \quad a + b = 7,~ ab=\dfrac{299}{21} \\\\ &=& \dfrac{7*21}{299} \\\\ \mathbf{ \dfrac{1}{a} + \dfrac{1}{b} } &=& \mathbf{ \dfrac{147}{299} } \\ \hline \end{array}$$