If. (a + 1/a) whole square =3. ; a is not equal to 0

Show that: a cube + 1/a cube = 0

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Solution

Given (a+1/a)² = 3
Therefore (a + 1/a) = √3
Recall the formula, (a³ + b³) = (a + b)³ - 3ab(a + b)
Therefore, (a³ + 1/a³) = (a + 1/a)³ - 3 * a * 1/a (a + 1/a)
= (√3)³ - 3(√3) = 3√3 - 3√3 = 0

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