The valueof 3 5 - 2-13 - 3 5 - 2-13 is -

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Expansion of (a ± b ± c)²

The valueof ...

Question

The value
of $\sqrt[3]{5 + 2 \sqrt{13}} + \sqrt[3]{5 - 2 \sqrt{13}}$ is =

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\frac{5 + \sqrt{3}}{5 - \sqrt{3}} + \frac{5 - \sqrt{3}}{5 + \sqrt{3}}

\frac{1}{2 + \sqrt{3}} + \frac{2}{\sqrt{5} - \sqrt{3}} + \frac{1}{2 - \sqrt{5}}

\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{3}{\sqrt{5} + \sqrt{2}}

35 - {15 + 14 - (13 + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (2 - 1 + 3)}

\frac{2 - m}{m + 7} = \frac{- 3}{5}

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

\frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36}) = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36}

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