Multiple choice

Calculate the value of $\alpha+\dfrac{1}{\alpha}$ where $'\alpha'$ is a root of equation $x^2-2bx+1=0$.

  1. $0$
  2. $2b$
  3. $-2b$

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given x^2 - 2bx + 1 = 0, divide by x: x - 2b + 1/x = 0. Thus, x + 1/x = 2b.

AI explanation

Using the given root alpha in the equation x^2 - 2bx + 1 = 0, we can write alpha^2 - 2b(alpha) + 1 = 0. Dividing the entire equation by alpha gives alpha - 2b + 1/alpha = 0. Rearranging the terms yields alpha + 1/alpha = 2b.

Keep practicing — related questions