Question

x²+1/x²=23 find x-1/x​

Answer 1

Answer:

w5ursjtsjydlufoysmgm

Answer 2

Answer:

The answer to this question is $\sqrt{21}$

Step-by-step explanation:

We know that,

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

Given that,

$x^2 + \frac{1}{x^2} = 23\\\\or, (x-\frac{1}{x})^2 + 2\cdot x\cdot \frac{1}{x} = 23\\\\or, (x-\frac{1}{x})^2 +2 = 23\\\\or,(x-\frac{1}{x})^2 = 21\\or,x-\frac{1}{x} = \sqrt{21}$

Similarly,

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