Question

Solve x + 1 / x = √ 5 , find the value of x2 + 1 / x2​

Answer 1

Solution:

✪ Given that, x+1/x = √5.

✪ From the given, we need to find the value of x²+1/x².

✪ The main concept involved here is using algebraic identity. Now, let us use the following identity to solve the question:

⇒ (a+b)² = a²+b²+2ab

Similarly,

⇒ (x+1/x)² = x²+1/x²+2(x)(1/x)

⇒ (√5)² = x²+1/x²+2

⇒ 5 = x²+1/x²+2

⇒ 5-2 = x²+1/x²

⇒ 3 = x²+1/x²

⇒ x²+1/x² = 3

Final Answer:

Hence, the value of x²+1/x² is 3.

Know more:

⇒ (a+b)² = a²+b²+2ab

⇒ (a-b)² = a²+b²-2ab

⇒ a²-b² = (a+b)(a-b)