Question

Given, x + 1/x = 5, then determine the value of x² + 1/x².

• A. 25
• B. 24
• C. 26
• D. 23

Answer 1

Answer:

D. 23

Given:

$x + \frac{1}{x} = 5$

Square both sides:

$\left(x + \frac{1}{x}\right)^2 = 5^2$

$x^2 + 2 + \frac{1}{x^2} = 25$

Now subtract 2:

$x^2 + \frac{1}{x^2} = 25 - 2 = 23$

Final Answer:

$\boxed{23}$