If the sum of a number and its reciprocal is 5/2 Then what is the value of thesum of their squares?

Question

Then what is the value of the sum of their squares?

🧐 Not the exact question you are looking for?Go ask a question

Let's denote the number as x. Then its reciprocal is 1/x.

According to the problem, we have:

x + 1/x = 5/2

We need to find the value of x^2 + (1/x)^2.

First, let's square both sides of the equation:

(x + 1/x)^2 = (5/2)^2

Expanding the left side, we get:

x^2 + 2 + 1/x^2 = 25/4

We are interested in the value of x^2 + 1/x^2, so let's subtract 2 from both sides:

x^2 + 1/x^2 = 25/4 - 2 = 9/4

So, the sum of the squares of the number and its reciprocal is 9/4.

This problem has been solved

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.