Question

please answer the question​

Answer 1

Given :-

▪ x + 1/x = 3

To Find :-

▪ x² + 1/x²

Solution :-

Given that,

⇒ x + 1/x = 3

Squaring both sides,

⇒ (x + 1/x)² = 3²

⇒ x² + 1/x² + 2 • x • 1/x = 9

[ ∵ (a + b)² = a² + b² + 2ab ]

⇒ x² + 1/x² + 2 = 9

⇒ x² + 1/x² = 9 - 2

⇒ x² + 1/x² = 7

Hence, The value of x² + 1/x² is 7

when, x + 1/x = 3

Extra Information :-

In the same way, if we were to find the value of x³ + 1/x³ , It could be calculated in the following way,

⇒ x + 1/x = 3

Raising to the power of 3, both sides

⇒ (x + 1/x)³ = 3³

⇒ x³ + 1/x³ + 3 • x • 1/x (x + 1/x) = 27

[ ∵ (a + b)³ = a³ + b³ + 3ab(a + b) ]

⇒ x³ + 1/x³ + 3×3 = 27 [ x + 1/x = 3 ,given ]

⇒ x³ + 1/x³ = 27 - 9

⇒ x³ + 1/x³ = 18