1.

If a + B=5 and a3 + B3=35​

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If a+b=5 and a3+b3=35, what is a5+b5?

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8 years ago

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a + b = 5 → a = 5 - b

a³ + b³ = 35 → you know that: a = 5 - b

(5 - b)³ + b³ = 35

[(5 - b)²(5 - b)] + b³ = 35

[(25 - 10b + b²)(5 - b)] + b³ = 35

[125 - 25b - 50b + 10b² + 5b² - b³] + b³ = 35

125 - 75b + 15b² = 35

15b² - 75b + 90 = 0

b² - 5b + 6 = 0

Polynomial like: ax² + bx + c, where:

a = 1

b = - 5

c = 6

Δ = b² - 4ac (discriminant)

Δ = (- 5)² - 4(1 * 6) = 25 - 24 = 1

x1 = (- b - √Δ) / 2a = (5 - 1) / (2 * 1) = 2

x2 = (- b + √Δ) / 2a = (5 + 1) / (2 * 1) = 3

Recall: a = 5 - b

First CASE: b = 2 → a = 3

Second case: b = 3 → a = 2

→ a^5 + b^5 = 3^5 + 2^5 = 243+ 32 = 275


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