Question

if x+1÷x=5 then x^2+1÷x^2=? ​

Answer 1

Solution :-

x + 1/x = 5

Squaring on both sides

⇒ (x + 1/x)² = 5²

⇒ (x)² + (1/x)² + 2(x)(1/x) = 25

[ Because (a + b)² = a² + b² + 2ab ]

⇒ x² + 1²/x² + 2 = 25

⇒ x² + 1/x² + 2 = 25

⇒ x² + 1/x² = 25 - 2

⇒ x² + 1/x² = 23

Therefore the value of x² + 1/x² is 23.

Answer 2

Question :-

$\sf \: \: if \: \: \: x + \frac{1}{x} = 5 \: then \: {x}^{2} + \frac{1}{ {x}^{2} } =$

Answer :-

$\red{ \leadsto} \boxed{ \sf \green{ {x}^{2}} + \orange{ \frac{1}{ {x}^{2} }} = 23} \:$

Formula used :-

→ (a + b)² = a² + b² + 2ab

Explanation :-

We have :

$\leadsto \sf x + \frac{1}{x} = 5 \\ \\ \mathfrak{ squaring \: on \: both \: sides} \\ \\ \leadsto \sf { \bigg (x + \frac{1}{x} \bigg) }^{2} = {5}^{2} \\ \\ \leadsto \sf {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 25 \\ \\ \leadsto \sf{ \: {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 25} \\ \\ \leadsto \sf {x}^{2} + \frac{1}{ {x}^{2} } = 25 - 2 \\ \\ \leadsto \boxed{ \sf{x}^{2} + \frac{1}{ {x}^{2} } = 23}$

Hope it will help you .