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Solve this question ​-example-1

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Explanation:

(a + 1/a)³ = a³ + 3a + 3/a + 1/a³

We are given that a + 1/a = 4, so we can substitute that into the identity and simplify:

(a + 1/a)³ = (4)³ = 64

a³ + 3a + 3/a + 1/a³ = 64

a³ + 1/a³ + 3(a + 1/a) = 64

a³ + 1/a³ + 3(4) = 64

a³ + 1/a³ = 52

Therefore, we have proved that a³ + 1/a³ = 52 when a + 1/a = 4.

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