If a + b = 3 and a^2 + b^2 = 7, what is a^4 + b^4?

Question

If a + b = 3 and a2 + b2 = 7, what is a4 + b4?

A. 45

B. 13

C. 35

D. 47

Answer: D. 47

Solution:

(a² + b²)² = 7²

=> 49 = a⁴ + b⁴ + 2a²b² …(1)

(a + b)² = 3²

=> 9 = a² + b² + 2ab = 7 + 2ab

Then 2ab = 9 – 7 = 2,

ab = 1

In (1), we have : a⁴ + b⁴ + 2 = 49

Finally, the answer a⁴ + b⁴ is 47.

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