Question

If x^2+1/x=5/2 find the value of x-1/x

Answer 1

Answer:

(1/2)^1/2

Step-by-step explanation:

x^2 + 1/x^2 =5/2

subtracting 2 on both sides,

x^2 + 1/x^2 -2= 5/2 -2 .... equation 1

observe that ,

(x - 1/x)^2 = x^2 -2*(x)*(1/x) + 1/x^2= x^2 + 1/x^2 -2

which is same as equation 1, hence putting this value

(x - 1/x)^2 = 5/2 -2

(x - 1/x)^2 = 1/2

x - 1/x = (1/2)^1/2

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Answer 2

Given :

$\frac{{x}^{2} + 1}{x} = \frac{5}{2}$

To find :

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

Solution :

$\frac{ {x}^{2} + 1 }{ \times } = \frac{5}{2} \\ \\ by \: \: cross \: \: multiplying \: \: we \: get \: \\ \\2( {x}^{2} + 1) = 5 \times x \\ \\ 2 {x}^{2} + 2 = 5 x \\ \\ 2 {x}^{2} - 5x + 2 = 0 \\ \\ 2 {x}^{2} - 4x - x + 2 = 0 \\ \\ 2x(x - 2) - 1(x - 2) = 0 \\ \\ (x - 2)(2x - 1) = 0 \\ \\ \\ x = 2 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: x = \frac{1}{2}$

If x = 2 then ,,,,

$= \frac{x - 1}{x} \\ \\ = \frac{2 - 1}{2} \\ \\ \frac{1}{2}$

If x = 1/2 then ,,,,

$= \frac{x - 1}{x} \\ \\ = \frac{ \frac{1}{2} - 1}{ \frac{1}{2} } \\ \\ = \frac{ \frac{1 - 2}{2} }{ \frac{1}{2} } \\ \\ = \frac{ - 1}{2} \times \frac{2}{1} \\ \\ = \frac{ - 1}{1} \\ \\ = - 1$

$\frac{x - 1}{x} = \frac{1}{2} \\</strong></p><p><strong> \frac{x - 1}{x} = - 1$

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