Question

pls help me solve it
pls​

Answer 1

Answer:

Sol i》

${x}^{2} + \frac{1}{ {x}^{2} } = 23 \\ add \: 2 \: or \: 2 \times x \times \frac{1}{x} \: to \: both \: side \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2x \times \frac{1}{x} = 23 + 2 \\ {(x + \frac{1}{x}) }^{2} = 25 = ( \frac{ + }{} 5) {}^{2} \\ (x + \frac{1}{x} ) = \frac{ + }{} 5$

Sol ii》

${x}^{2} + \frac{1}{ {x}^{2} } = 23 \\ subtract \: 2 \: or \: 2x \times \frac{1}{x} \: to \: both \: side \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2x \times \frac{1}{x} = 23 - 2 \\ (x - \frac{1}{x} ) {}^{2} = 21 \\ (x - \frac{1}{x} ) = \frac{ + }{} \sqrt{21}$

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Answer 2

Answer:

I hope it helps you!!

Step-by-step explanation:

solution,

case (i)

x^2 + 1 /x^2 = 23

or, (x + 1 /x)^2 - 2x ×1 /x = 23

or, (x + 1 /x)^2 - 2 = 23

or, (x + 1 /x)^2 = 25

or, (x + 1 /x) = √25

so, (x + 1 /x) = 5

case (ii)

x^2 - 1 /x^2 = 23

or, (x + 1 /x)( x - 1/x) = 23

substituting the value of (x + 1 /x) from (i)

or, 5 (x -1 /x) = 23

so, (x - 1 /x) = 23/5