## Question

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

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

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.**