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Q5 (CISF/2021) Science & Technology › Basic Science (Physics, Chemistry, Biology)

If the sum of a real number and its reciprocal is equal to 5, then what is the sum of the squares of the number and its reciprocal ?

Result
Your answer: —  Â·  Correct: C

Explanation

Let the real number be x. According to the problem, the sum of the number and its reciprocal is 5:
x + 1/x = 5

We need to find the sum of the squares of the number and its reciprocal, which is x2 + (1/x)2. To do this, we square both sides of the initial equation:

(x + 1/x)2 = 52

Applying the algebraic identity (a + b)2 = a2 + b2 + 2ab, we get:
x2 + (1/x)2 + 2(x)(1/x) = 25
x2 + 1/x2 + 2 = 25

Subtracting 2 from both sides of the equation:
x2 + 1/x2 = 25 - 2
x2 + 1/x2 = 23

Thus, the sum of the squares of the number and its reciprocal is 23.

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