If a + b = 5 and ab = 6, what is a⁵ + b⁵?

275. a² + b² = 13, a³ + b³ = 125 − 90 = 35. a⁵ + b⁵ = (a² + b²)(a³ + b³) − a²b²(a + b) = 455 − 180 = 275. (2⁵ + 3⁵ = 32 + 243.)

If $a + b = 5$ and $ab = 6$ , what is $a^{5} + b^{5}$ ?

Competition practiceAlgebra

a^{2} + b^{2} = 13, a^{3} + b^{3} = 125 - 90 = 35. a^{5} + b^{5} = (a^{2} + b^{2}) (a^{3} + b^{3}) - a^{2} b^{2} (a + b) = 455 - 180 = 275. (2^{5} + 3^{5} = 32 + 243.)

Answer: A) 275

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