3. Given that

Question

(𝑥 − 𝐴)2 + 𝐵 = 𝑥2 − 10𝑥 +
29, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴 + 𝐵
A. -9
B.-1
C.8
D. 9

Answer 1

Expanding the left side of the equation, we get:

𝑥2 - 2𝐴𝑥 + 𝐴2 + 𝐵 = 𝑥2 - 10𝑥 + 29

Rearranging terms and simplifying, we get:

2𝐴𝑥 = 10𝑥 - 𝐴2 - 𝐵 + 29

𝑥 = 5 - (𝐴2 + 𝐵 - 29)/2𝐴

To find the value of 𝐴 + 𝐵, we need to substitute 𝑥 = 𝐴 into the original equation:

(𝐴 - 𝐴)2 + 𝐵 = 𝐴2 - 10𝐴 + 29

Simplifying, we get:

𝐵 = -9𝐴 + 29

Substituting this expression for 𝐵 into the first equation, we get:

𝑥2 - 2𝐴𝑥 + 𝐴2 - 9𝐴 + 29 = 𝑥2 - 10𝑥 + 29

Simplifying and rearranging, we get:

𝐴 = 9

Substituting this value of 𝐴 into the equation we found for 𝐵, we get:

𝐵 = -9(9) + 29 = -64

Therefore, 𝐴 + 𝐵 = 9 - 64 = -55

The answer is not among the options provided.