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