Problem: If y=a+bxy=a+\dfrac{b}{x}y=a+xb, where a‾\underline{a}a and b‾\underline{b}b are constants, and if y=1y=1y=1 when x=−1x=-1x=−1, and y=5y=5y=5 when x=−5x=-5x=−5, then a+ba+ba+b equals:
Answer Choices:
A. −1-1−1
B. 000
C. 111
D. 101010
E. 111111 Solution:
y=a+bxy = a + \dfrac{b}{x} y=a+xb
1=a−b1 = a - b 1=a−b
5=a−15b5 = a - \dfrac{1}{5} b 5=a−51b
∴b=5anda=6\quad \therefore \quad b = 5 \quad \text{and} \quad a = 6 ∴b=5anda=6