Question

(x+1/x)=4 find (x-1/x)​

Answer 1

Answer:

2

Step-by-step explanation:

x+1/x=4 First let's solve the first equation

x+1=4x Cross multiplication

4x-x=1 Transposition

3x=1

x=1/3 Cross multiplication

1/3-1/1/3=2/3 ÷ 1/3=

2/3×3/1= 2 (/ actually means the line between numerator and denominator of a fraction so don't get confused!)

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EZ

Answer 2

Given :-

$\bf x + \frac{1}{x} = 4$

To find :-

$\bf x - \frac{1}{x} = \: ?$

Solution :-

$\huge \tt x + \frac{1}{x } = 4 \\ \\ = > \: \: { \bigg(x + \frac{1}{x} \bigg)}^{2} = {(4)}^{2} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 = 14$

Now,

${ \bigg(x - \frac{1}{x} \bigg)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ \\ = > (14) - 2 \: \: \: \: = {12} \\ \\ \Large{ \boxed{\boxed{ \sf{ x - \frac{1}{x}=\red{\sqrt{12}} \: \: or \: \: \red{2\sqrt{3}}}}}}$