Question

if (a+1/a)²=b, then a³ +1/a³=?

Answer 1

From the given info we know (a + 1/a)= √b ...(1)

Consider (a + 1/a)^3 = a^3 + 1/a^3 + 3(a + 1/a)

Hence a^3 + 1/a^3 = (a + 1/a)^3 - 3(a + 1/a)   ...(2)

Putting 1 in 2, we get

a^3 + 1/a^3 = b√b -3√b

Hence your answer is √b(b-3)

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