Question

if x^2+1/x^2=23,find the value ofx+1/x​

Answer 1

Answer:

Hence the answer is

$x + \frac{1}{x} = 5$

Step-by-step explanation:

${x}^{2} + \frac{1}{ {x}^{2} } = 23 \\ add \: 2 \: on \: both \: side \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 23 + 2 \\ ( {x + \frac{1}{x} })^{2} = 25 \\ taking \: square \: root \: on \: both \: side \\ x + \frac{1}{x} = \sqrt{25} \\ x + \frac{1}{x} = 5$

Answer 2

Answer:

$x + \frac{1}{x} = 5$

Step-by-step explanation:

We have

${x}^{2} + \frac{1}{ {x}^{2} } = 23$

We know

${a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

So,

${x}^{2} + \frac{1}{ {x}^{2} } = 23 \\ {(x + \frac{1}{x}) }^{2} - 2 \times x \times \frac{1}{x} = 23 \\ {(x + \frac{1}{x}) }^{2} = 23 + 2 \\ x + \frac{1}{x} = \sqrt{25} = 5$