Question

If =
1/
√5−2
then find the value of x²-1/x² and x³+1/x³

*FIRST ANSWER WILL GET A FOLLOWER*​

Answer 1

Answer:

x= √5 - 2

⇒ 1/x = 1/ √5 - 2

⇒ 1/x = 1/ √5 - 2 × √5 + 2/ √5 + 2

⇒ 1/x = √5 + 2 / (√5)² - (2)²

⇒ 1/x = √5 + 2 / 5 - 4

⇒ 1/x = √5 + 2

Now,

x + 1/x = √5 - 2 + √5 + 2

x + 1/x = 2√5

And, on squaring both sides,

(x + 1/x )² = (2√5) ²

⇒ x² + 1 / x² + 2 = 20

⇒ x² + 1 / x² = 20 - 2

⇒ x² + 1 / x² = 18