Question

If x+1/x=3then the value of x is .......

Answer 1

Nice question!


In this question we will use the identity,

(a + b)² = a² + b² + 2ab

Given that,

$x + \frac{1}{x} = 3 \\ \\ = > (x + \frac{1}{x} ) {}^{2} = {3}^{2} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 9 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 7$

Now Subtract 2 × x × 1/x from both sides

=>
${x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} = 7 - 2 \times x \times \frac{1}{x} \\ \\ = > (x - \frac{1}{x} ) {}^{2} = 7 - 2 \\ \\ = > (x - \frac{1}{x} ) {}^{2} = 5 \\ \\ = > x - \frac{1}{x} = \sqrt{5}$


Now x + 1/x = 3

and x - 1/x = √5

Adding them we get,


x + 1/x + x - 1/x = 3 + √5

=> 2x= 3 + √5

=>
$x = \frac{3 + \sqrt{5} }{2}$
Hope it helps dear friend ☺️✌️

Answer 2

Answer:

x plus 3

Explanation: