Question

if X+1/x=√5, find the value of (x²+1/x²)

full and clear explanation please

if bad answer is given I will report immediately

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Answer 1

The value of x^2 + (1/x^2) is 3.

Step-by-step explanation:

Given:

x + (1/x) = √5

To find:

the value of x^2 + (1/x^2) = ?

Solution:

We have,

x + (1/x) = √5

Squaring on both sides, we get

=> [x + (1/x)]^2 = (√5)^2

since, (a + b)^2 = a^2 + 2ab + b^2

Where, a = x and b = 1/x,

Now, we get

=> [(x)^2 + 2(x)(1/x) + (1/x)^2 = (√5)^2

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

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

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

=> x^2 + (1/x^2) = 3

Answer:

Hence, the value of x^2 + (1/x^2) is 3.